Data processing apparatus and data processing method

ABSTRACT

The present technology relates to a data processing apparatus and a data processing method which enable provision of an LDPC code that achieves good error-rate performance. 
     An LDPC encoding unit performs encoding using an LDPC code having a code length of 64800 bits and a code rate of 18/30, 19/30, 20/30, 21/30, 22/30, or 23/30. The LDPC code includes information bits and parity bits, and a parity check matrix H is composed of an information matrix portion corresponding to the information bits of the LDPC code, and a parity matrix portion corresponding to the parity bits. The information matrix portion of the parity check matrix H is represented by a parity check matrix initial value table that shows positions of elements of 1 in the information matrix portion in units of 360 columns. The present technology may be applied to LDPC encoding and LDPC decoding.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No. 15/935,760, filed Mar. 26, 2018, which is a continuation of U.S. patent application Ser. No. 14/386,868, filed Sep. 22, 2014, which is a National Stage of PCT/JP2014/051623, filed Jan. 27, 2014, and claims the benefit of priority under 35 U.S.C. § 119 of Japanese Patent Application No. 2013-023882, filed Feb. 8, 2013. The entire contents of each of the above-noted documents are incorporated herein by reference.

TECHNICAL FIELD

The present technology relates to data processing apparatuses and data processing methods, and more specifically to data processing apparatuses and data processing methods which enable provision of, for example, LDPC codes that achieve good error-rate performance.

BACKGROUND ART

In recent years, LDPC (Low Density Parity Check) codes, which have a high error-correcting capability, have been widely employed in transmission schemes including satellite digital broadcasting technologies, such as DVB (Digital Video Broadcasting)-S.2, which is used in Europe (see, for example, NPL 1). LDPC codes are also employed in next-generation terrestrial digital broadcasting technologies, such as DVB-T.2.

Recent studies have found that, like turbo codes, LDPC codes have a performance closer to the Shannon limit for larger code lengths. In addition, because of their characteristic of having minimum distances proportional to code lengths, LDPC codes have the feature of high block error probability performance, and have a further advantage in showing substantially no error floor phenomena, which is observed in the decoding characteristics of turbo codes and the like.

LDPC codes will now be described in more detail. LDPC codes are linear codes, and may or may not be binary. The following description will be given in the context of binary LDPC codes.

An LDPC code has the most striking feature that it is defined by a sparse parity check matrix. Here, the term “sparse matrix” refers to a matrix having a very small number of elements of 1 (or a matrix whose elements are almost zeros).

FIG. 1 illustrates an example of a parity check matrix H of an LDPC code.

In the parity check matrix H illustrated in FIG. 1, the weight of each column (column weight) (i.e., the number of 1s) is 3 and the weight of each row (row weight) is 6.

In an encoding operation using an LDPC code (LDPC encoding), for example, a generator matrix G is generated on the basis of a parity check matrix H. By multiplying the generator matrix G by binary information bits, a code word (i.e., an LDPC code) is generated.

Specifically, an encoding device that performs LDPC encoding first calculates a generator matrix G, where the equation GH^(T)=0 is established between the transpose H^(T) of the parity check matrix H and the generator matrix G. Here, if the generator matrix G is a K×N matrix, the encoding device multiplies the generator matrix G by a bit sequence (i.e., a vector u) of K information bits to generate a code word c (=uG) having N bits. The code word (or LDPC code) generated by the encoding device is received on the receiver side via a certain communication path.

An LDPC code can be decoded using the message passing algorithm, which is an algorithm called probabilistic decoding proposed by Gallager and which is based on belief propagation on a so-called Tanner graph with variable nodes (also referred to as “message nodes”) and check nodes. Here, the variable nodes and the check nodes will also be hereinafter referred to simply as “nodes” as appropriate.

FIG. 2 illustrates an LDPC code decoding procedure.

Note that, in the following description, a real-number value representing the likelihood of the value “0” of the i-th bit of an LDPC code (i.e., a code word) received on the receiver side, which is expressed in log likelihood ratio (i.e., a reception LLR), is also referred to as a “reception value u_(0i)” as appropriate. Further, a message output from a check node is represented by u_(j), and a message output from a variable node is represented by v_(i).

In an LDPC code decoding process, first, as illustrated in FIG. 2, in step S11, an LDPC code is received, and a message (check node message) u_(j) is initialized to “0”. In addition, a variable k of a counter for repetitive processing, which takes an integer value, is initialized to “0”. Then, the process proceeds to step S12. In step S12, a message (variable node message) v_(i) is determined by performing computation given by Expression (1) (variable node computation) on the basis of a reception value u_(0i) obtained through the reception of the LDPC code. A message u_(j) is further determined by performing computation given by Expression (2) (check node computation) on the basis of the message v_(i).

$\begin{matrix} \left\lbrack {{Math}.\mspace{14mu} 1} \right\rbrack & \; \\ {v_{i} = {u_{0i} + {\sum\limits_{j = 1}^{d_{v} - 1}u_{j}}}} & (1) \\ \left\lbrack {{Math}.\mspace{14mu} 2} \right\rbrack & \; \\ {{\tanh \left( \frac{u_{j}}{2} \right)} = {\prod\limits_{i = 1}^{d_{c} - 1}{\tanh \left( \frac{v_{i}}{2} \right)}}} & (2) \end{matrix}$

Here, d_(v) and d_(c) in Expressions (1) and (2) are arbitrarily selectable parameters indicating the number of is in the vertical direction (columns) and the horizontal direction (rows) of the parity check matrix H, respectively. For example, for an LDPC code in a parity check matrix H with a column weight of 3 and a row weight of 6 (i.e., a (3,6) LDPC code) illustrated in FIG. 1, d_(v)=3 and d_(c)=6.

Note that, in each of the variable node computation of Expression (1) and the check node computation of Expression (2), a message input from an edge (or a line connecting between a variable node and a check node) from which a message is output is not the target of the computation. Thus, the range of computation is 1 to d_(v)−1 or 1 to d_(c)−1. Furthermore, the check node computation of Expression (2) is actually performed by creating in advance a table of a function R(v₁, v₂) given by Expression (3), which is defined by one output for two inputs v₁ and v₂, and sequentially (or recursively) using the table in the manner given by Expression (4).

[Math. 3]

x=2 tanh⁻¹{tanh(v ₁/2)tanh(v ₂/2)}=R(v ₁ v ₂)   (3)

[Math. 4]

u _(j) =R(v ₁ ,R(v ₂ ,R(v ₃ , . . . R(v _(d) _(c) ⁻² ,v _(d) _(c) ⁻¹))))   (4)

In step S12, furthermore, the variable k is incremented by “1”. Then, the process proceeds to step S13. In step S13, it is determined whether the variable k is larger than a certain number of times of repetitive decoding C. If it is determined in step S13 that the variable k is not larger than C, the process returns to step S12, and subsequently, similar processing is repeatedly performed.

If it is determined in step S13 that the variable k is larger than C, the process proceeds to step S14. In step S14, a message v_(i) as a final output result of decoding is determined by performing computation given by Expression (5), and is output. Then, the LDPC code decoding process ends.

$\begin{matrix} \left\lbrack {{Math}.\mspace{14mu} 5} \right\rbrack & \; \\ {v_{i} = {u_{0i} + {\sum\limits_{j = 1}^{d_{v}}u_{j}}}} & (5) \end{matrix}$

Here, the computation of Expression (5) is performed using, unlike the variable node computation of Expression (1), the messages u_(j) from all the edges connected to a variable node.

FIG. 3 illustrates an example of a parity check matrix H of a (3,6) LDPC code (with a code rate of 1/2 and a code length of 12).

In the parity check matrix H illustrated in FIG. 3, similarly to FIG. 1, the column weight is 3 and the row weight is 6.

FIG. 4 illustrates a Tanner graph of the parity check matrix H illustrated in FIG. 3.

Here, in FIG. 4, a check node is represented by a plus “+” sign, and a variable node is represented by an equal “=” sign. A check node and a variable node correspond to each row and column of the parity check matrix H, respectively. A connection between a check node and a variable node is an edge, and corresponds to an element of “1” in the parity check matrix.

More specifically, in a case where the element in the j-th row and the i-th column of the parity check matrix is 1, in FIG. 4, the i-th variable node (“=” node) from the top and the j-th check node (“+” node) from the top are connected by an edge. An edge indicates that a code bit corresponding to a variable node has a constraint corresponding to a check node.

In the sum product algorithm, which is an LDPC code decoding method, variable node computation and check node computation are repeatedly performed.

FIG. 5 illustrates variable node computation to be performed at a variable node.

At a variable node, a message v_(i) corresponding to an edge for which calculation is to be performed is determined through the variable node computation of Expression (1) using messages u₁ and u₂ from the remaining edges connected to the variable node and also using a reception value u_(0i). The messages corresponding to the other edges are also determined in a similar way.

FIG. 6 illustrates check node computation to be performed at a check node.

Here, the check node computation of Expression (2) can be rewritten as Expression (6) by using the relationship of the equation a×b=exp{ln(|a|)+ln(|b|)}×sign(a)×sign(b), where sign(x) is 1 for x≥0 and −1 for x<0.

$\begin{matrix} \left\lbrack {{Math}.\mspace{14mu} 6} \right\rbrack & \; \\ \begin{matrix} {u_{j} = {2{\tanh^{- 1}\left( {\prod\limits_{i = 1}^{d_{c} - 1}{\tanh \left( \frac{v_{i}}{2} \right)}} \right)}}} \\ {= {2{\tanh^{- 1}\left\lbrack {\exp \left\{ {\sum\limits_{i = 1}^{d_{c} - 1}{\ln \left( {{\tanh \left( \frac{v_{i}}{2} \right)}} \right)}} \right\} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\left( {\tanh \left( \frac{v_{i}}{2} \right)} \right)}}} \right\rbrack}}} \\ {= {2{\tanh^{- 1}\left\lbrack {\exp \left\{ {- \left( {\sum\limits_{i = 1}^{d_{c} - 1}{- {\ln \left( {\tanh \left( \frac{v_{i}}{2} \right)} \right)}}} \right)} \right\}} \right\rbrack} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\left( v_{i} \right)}}}} \end{matrix} & (6) \end{matrix}$

If the function ϕ(x) is defined as the equation ϕ(x)=ln(tanh(x/2)) for x≥0, the equation ϕ⁻¹(x)=2 tanh⁻¹(e^(−x)) is established. Thus, Expression (6) can be transformed into Expression (7).

$\begin{matrix} \left\lbrack {{Math}.\mspace{14mu} 7} \right\rbrack & \; \\ {u_{j} = {{\varphi^{- 1}\left( {\sum\limits_{i = 1}^{d_{c} - 1}{\varphi \left( {v_{i}} \right)}} \right)} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\left( v_{i} \right)}}}} & (7) \end{matrix}$

At a check node, the check node computation of Expression (2) is performed in accordance with Expression (7).

More specifically, at a check node, as illustrated in FIG. 6, a message u_(j) corresponding to an edge for which calculation is to be performed is determined through the check node computation of Expression (7) using messages v₁, v₂, v₃, v₄, and v₅ from the remaining edges connected to the check node. The messages corresponding to the other edges are also determined in a similar way.

Note that the function ϕ(x) in Expression (7) can be represented by the equation ϕ(x)=ln((e^(x)+1)/(e^(x)−1)), where ϕ(x)=ϕ⁻¹(x) for x>0. The functions ϕ(x) and ϕ⁻¹(x) may be implemented in hardware by using an LUT (Look Up Table), where the same LUT is used for both functions.

CITATION LIST Non Patent Literature

-   NPL 1: DVB-S.2: ETSI EN 302 307 V1.2.1 (2009-08)

SUMMARY OF INVENTION Technical Problem

In the standards that employ LDPC codes, such as DVB-S.2, DVB-T.2, and DVB-C.2, an LDPC code is mapped to symbols (or is symbolized) of orthogonal modulation (digital modulation) such as QPSK (Quadrature Phase Shift Keying). The symbols are mapped to constellation points and are transmitted.

Meanwhile, there has recently been a demand for efficient transmission of a large amount of data such as a three-dimensional (3D) image or a 4k image. A 4k image has a resolution of 3840 pixels horizontally and 2160 pixels vertically, providing approximately four times the pixel resolution of full high definition.

However, prioritizing the efficiency of data transmission would increase an error rate.

On the contrary, there may also be a demand that the efficiency of data transmission can be somewhat sacrificed for data transmission with good error-rate performance.

In the future, demands for data transmission with various efficiency levels are expected to increase. For example, a plurality of LDPC codes having different code rates allow data transmission with various efficiency levels.

In data transmission, therefore, it is desirable that LDPC codes having code rates which are easily set to a somewhat large number of code rates, the number of which is greater than or equal to, for example, the number of code rates demanded for data transmission, be employed.

It is also desirable that LDPC codes have high resistance to errors (i.e., high robustness), that is, good error-rate performance, no matter which code rate of LDPC code is to be employed.

The present technology has been made in view of the foregoing situation, and is intended to provide LDPC codes having good error-rate performance.

Solution to Problem

A first data processing apparatus or data processing method of the present technology includes an encoding unit configured to encode or an encoding step of encoding information bits into an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 18/30 on the basis of a parity check matrix of the LDPC code, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns, including

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A second data processing apparatus or data processing method of the present technology includes a decoding unit configured to decode or a decoding step of decoding an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 18/30 on the basis of a parity check matrix of the LDPC code, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns, including

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73 605 872 4008 6279 7653 10346 10799 12482 12935 13604 15909 16526 19782 20506 22804 23629 24859 25600

1445 1690 4304 4851 8919 9176 9252 13783 16076 16675 17274 18806 18882 20819 21958 22451 23869 23999 24177

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2223 17905 25484

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A third data processing apparatus or data processing method of the present technology includes an encoding unit configured to encode or an encoding step of encoding information bits into an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 19/30 on the basis of a parity check matrix of the LDPC code, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns, including

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14930 15004 19622

15 9351 22137

6984 10545 18086

17 5394 22378

5666 17493 23525

2788 2962 18427

15308 18638 23694

6477 21407 23683

5907 22795 23101

3398 17256 18334

3010 12780 18130

2912 12048 19907

10071 21798 22747

9806 23050 23683

13541 23317 23733

11998 12007 17363

9401 16372 23473

16221 19981 21929

32 7499 20187

17718 22377 23147

17276 21344 22014

21779 22541 23607

16248 18722 23096

4225 19889 20582

21394 23463 23652

10428 11323 12984

60 23098 23752

8941 12692 20396

3909 12976 23323

4172 13704 21088

4252 20334 23229

5669 9953 23616

747 22117 23391

1201 17300 19083

6226 22684 23382

8854 14713 23706

18391 19269 20334

15856 16811 23747

39 3964 14259

11159 17884 18130

11388 23637 23738

12481 16865 23422

17762 22000 23602

13515 19709 21596

45 16207 16302

2011 13753 23611

20451 23564 23756

13 10379 16323

20 14421 16684

11082 19565 22082

9158 9437 20186

9270 21333 22631

24 22736 23382

28 19129 21403

34 1541 19415

18638 22335 23418

42 8892 23629

13154 13353 22663

51 2780 21921

45 6677 20895

61 15836 22536

15246 23565 23578

48 22661 23012

17 21419 23698

22650 23448 23497

20671 22579 23692

27 7302 23401

9478 19287 20789

9312 23176 23598

3566 21768 23652

19 6707 11777

430 19822 22687

1705 6631 23312

5 19562 23680

644 2620 13917

3998 22493 23529

20916 22930 23741

12467 22100 23737

8546 15903 22828.

A fourth data processing apparatus or data processing method of the present technology includes a decoding unit configured to decode or a decoding step of decoding an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 19/30 on the basis of a parity check matrix of the LDPC code, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns, including

354 794 1214 1640 8278 9195 11069 11580 11911 13276 13438 14495 14734 15741 19195 19537 21951

4657 5351 5887 6634 7718 8327 10300 10815 11822 13506 16746 19429 19920 21548 22087 23650 23712

4603 5160 6345 7259 8428 8937 9665 11623 11864 13590 13613 17117 18678 19118 21126 21884 23054

27 2157 3039 3219 4191 5651 7098 12555 12634 13791 14885 15505 16163 16664 19792 20437 23588

30 49 2768 3314 4345 6972 8994 15294 16653 18282 18808 19324 20597 21510 21643 23741 23748

1 553 2228 4277 4499 5818 10580 10823 12135 14102 14923 15980 15995 16319 18577 22838 23058

4 2307 2764 3075 4755 8064 9673 12150 21139 21224 21572 21682 23415 23598 23703 23710 23739

4 9 13 5867 6028 7730 10859 14755 14879 15746 21166 21643 22777 23409 23502 23511 23734

13 28 481 7146 8144 13768 15081 19349 20187 20858 21913 22025 23134 23472 23506 23711 23744

12 24 36 1004 3080 3496 7356 7834 16011 16492 19536 20918 22833 22937 23717 23745 23749

31 378 812 1578 1957 5163 14759 16701 16829 18111 22931 23253 23314 23351 23584 23660 23699

25 38 1183 6573 9556 12523 14303 14412 18209 18530 21334 21770 21809 22630 22734 23154 23186

57 3497 6667 9653 10168 12771 15082 19365 19415 19514 19611 19785 21242 22974 23107 23690 23715

2456 2562 6223 7150 12652 14580 14807 20072 20513 21091 21201 21922 23010 23046 23215 23514 23663

5 635 3760 4981 6824 8425 13532 14618 19654 20026 21439 21684 22023 23027 23499 23691 23707

8 3018 4509 9002 11537 17156 17490 17779 20182 22018 22416 23348 23497 23575 23685 23708 23753

3 19 60 9502 12512 12907 17118 20225 20508 21429 21695 22010 22187 22347 23574 23608 23617

2 5 22 61 6583 15302 17930 18081 18562 19427 21204 21744 22713 23422 23503 23597 23730

15 4333 9774 11921 15075 20998 21581 21622 22468 22638 23104 23530 23593 23613 23645 23648 23719

16 48 65 2563 3079 12594 17391 17524 20302 21062 21809 22772 23189 23501 23625 23628 23756

59 4288 6124 13237 13580 13607 19899 20348 21481 22380 22510 22883 23114 23233 23709 23715 23735

46 2949 3278 6100 9887 10255 19509 19883 20022 21147 21422 21915 22489 22777 23422 23750 23754

761 8196 8895 23472

10842 15470 23658 23748

13 16585 19888 21445

13341 17522 18603 20826

2932 8194 19093 21220

6202 9623 23715

2288 21290 22116

5143 10529 19731

15559 16069 23704

137 11927 20849

11 5997 11214

1212 9635 22820

8785 10770 15217

14930 15004 19622

15 9351 22137

6984 10545 18086

17 5394 22378

5666 17493 23525

2788 2962 18427

15308 18638 23694

6477 21407 23683

5907 22795 23101

3398 17256 18334

3010 12780 18130

2912 12048 19907

10071 21798 22747

9806 23050 23683

13541 23317 23733

11998 12007 17363

9401 16372 23473

16221 19981 21929

32 7499 20187

17718 22377 23147

17276 21344 22014

21779 22541 23607

16248 18722 23096

4225 19889 20582

21394 23463 23652

10428 11323 12984

60 23098 23752

8941 12692 20396

3909 12976 23323

4172 13704 21088

4252 20334 23229

5669 9953 23616

747 22117 23391

1201 17300 19083

6226 22684 23382

8854 14713 23706

18391 19269 20334

15856 16811 23747

39 3964 14259

11159 17884 18130

11388 23637 23738

12481 16865 23422

17762 22000 23602

13515 19709 21596

45 16207 16302

2011 13753 23611

20451 23564 23756

13 10379 16323

20 14421 16684

11082 19565 22082

9158 9437 20186

9270 21333 22631

24 22736 23382

28 19129 21403

34 1541 19415

18638 22335 23418

42 8892 23629

13154 13353 22663

51 2780 21921

45 6677 20895

61 15836 22536

15246 23565 23578

48 22661 23012

17 21419 23698

22650 23448 23497

20671 22579 23692

27 7302 23401

9478 19287 20789

9312 23176 23598

3566 21768 23652

19 6707 11777

430 19822 22687

1705 6631 23312

5 19562 23680

644 2620 13917

3998 22493 23529

20916 22930 23741

12467 22100 23737

8546 15903 22828.

A fifth data processing apparatus or data processing method of the present technology includes an encoding unit configured to encode or an encoding step of encoding information bits into an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 20/30 on the basis of a parity check matrix of the LDPC code, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns, including

692 1779 1973 2726 5151 6088 7921 9618 11804 13043 15975 16214 16889 16980 18585 18648

13 4090 4319 5288 8102 10110 10481 10527 10953 11185 12069 13177 14217 15963 17661 20959

2330 2516 2902 4087 6338 8015 8638 9436 10294 10843 11802 12304 12371 14095 18486 18996

125 586 5137 5701 6432 6500 8131 8327 10488 11032 11334 11449 12504 16000 20753 21317

30 480 2681 3635 3898 4058 12803 14734 20252 20306 20680 21329 21333 21466 21562 21568

20 44 738 4965 5516 7659 8464 8759 12216 14630 18241 18711 19093 20217 21316 21490

31 43 3554 5289 5667 8687 14885 16579 17883 18384 18486 19142 20785 20932 21131 21308

7054 9276 10435 12324 12354 13849 14285 16482 19212 19217 19221 20499 20831 20925 21195 21247

9 13 4099 10353 10747 14884 15492 17650 19291 19394 20356 20658 21068 21117 21183 21586

28 2250 2980 8988 10282 12503 13301 18351 20546 20622 21006 21293 21344 21472 21530 21542

17 32 2521 4374 5098 7525 13035 14437 15283 18635 19136 20240 21147 21179 21300 21349

57 4735 5657 7649 8807 12375 16092 16178 16379 17545 19461 19489 20321 20530 21453 21457

35 55 5333 14423 14670 15438 19468 19667 20823 21084 21241 21344 21447 21520 21554 21586

13 20 2025 11854 12516 14938 15929 18081 19730 19929 20408 21338 21391 21425 21468 21546

54 7451 8176 10136 15240 16442 16482 19431 19483 19762 20647 20839 20966 21512 21579 21592

26 465 3604 4233 9831 11741 13692 18953 18974 21021 21039 21133 21282 21488 21532 21558

1 7 16 59 6979 7675 7717 9791 12370 13050 18534 18729 19846 19864 20127 20165

15 31 11089 12360 13640 14237 17937 18043 18410 19443 21107 21444 21449 21528 21576 21584

32 51 9768 17848 18095 19326 19594 19618 19765 20440 20482 20582 21236 21338 21563 21587

44 55 4864 10253 11306 12117 13076 13901 15610 17057 18205 19794 20939 21132 21267 21573

3436 11304 15361 16511 16860 18238 18639 19341 20106 20123 20407 21200 21280 21452 21526 21569

679 8822 11045 14403 16588 17838 19117 19453 20265 20558 21374 21396 21428 21442 21529 21590

391 13002 13140 14314 17169 17175 17846 18122 19447 20075 20212 20436 20583 21330 21359 21403

7601 10257 20060 21285

4419 9150 18097 20315

4675 13376 21435

610 1238 16704

5732 7096 21104

5690 13531 14545

4334 14839 17357

8 2814 17674

2392 8128 18369

502 7403 15133

343 13624 20673

13188 15687 21593

321 16866 21347

1242 4261 17449

4691 8086 8691

8500 11538 20278

6269 12905 18192

5984 15452 17111

11541 18717 21534

16 10780 16107

12310 12959 20390

1365 18306 19634

6125 19132 20242

3012 17233 21533

5816 13021 21440

13207 17811 18798

2762 7586 12139

3949 5545 13584

11374 18279 19241

2736 10989 21209

4095 20677 21395

8251 10084 20498

7628 8875 21406

2743 8943 9090

1817 7788 15767

9333 9838 21268

6203 9480 12042

5747 21187 21468

2553 18281 21500

3179 9155 15222

12498 18109 20326

14106 21209 21592

7454 17484 20791

20804 21120 21574

5754 18178 20935

30 4322 21381

11905 20416 21397

12452 19899 21497

1917 6028 16868

9891 18710 18953

912 21083 21446

370 14355 18069

16519 19003 20902

11163 17558 18424

8427 14396 21405

8885 11796 21361

4960 15431 20653

11944 16839 21236

9967 14529 17208

14144 19354 19745

7986 12680 21396

6097 11501 13028

33 13803 21038

3177 20124 20803

2692 6841 18655

971 5892 14354

3887 19455 21271

17214 17315 21148

6539 13910 21526

3809 5153 15793

3865 21438 21510

7129 17787 19636

5972 13150 14182

7078 14906 16911

15705 21160 21482

5479 13860 19763

16817 19722 20001

14649 16147 18886

15138 18578 21502

2096 2534 17760

11920 13460 19783

19876 20071 20583

6241 14230 20775

16138 16386 21371

8616 15624 18453

6013 8015 21599

9184 10688 20792

18122 21141 21469

10706 13177 20957

15148 15584 20959

9114 9432 16467

5483 14687 14705

8325 21161 21410

2328 17670 19834

7015 20802 21385

52 5451 20379

9689 15537 19733.

A sixth data processing apparatus or data processing method of the present technology includes a decoding unit configured to decode or a decoding step of decoding an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 20/30 on the basis of a parity check matrix of the LDPC code, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns, including

692 1779 1973 2726 5151 6088 7921 9618 11804 13043 15975 16214 16889 16980 18585 18648

13 4090 4319 5288 8102 10110 10481 10527 10953 11185 12069 13177 14217 15963 17661 20959

2330 2516 2902 4087 6338 8015 8638 9436 10294 10843 11802 12304 12371 14095 18486 18996

125 586 5137 5701 6432 6500 8131 8327 10488 11032 11334 11449 12504 16000 20753 21317

30 480 2681 3635 3898 4058 12803 14734 20252 20306 20680 21329 21333 21466 21562 21568

20 44 738 4965 5516 7659 8464 8759 12216 14630 18241 18711 19093 20217 21316 21490

31 43 3554 5289 5667 8687 14885 16579 17883 18384 18486 19142 20785 20932 21131 21308

7054 9276 10435 12324 12354 13849 14285 16482 19212 19217 19221 20499 20831 20925 21195 21247

9 13 4099 10353 10747 14884 15492 17650 19291 19394 20356 20658 21068 21117 21183 21586

28 2250 2980 8988 10282 12503 13301 18351 20546 20622 21006 21293 21344 21472 21530 21542

17 32 2521 4374 5098 7525 13035 14437 15283 18635 19136 20240 21147 21179 21300 21349

57 4735 5657 7649 8807 12375 16092 16178 16379 17545 19461 19489 20321 20530 21453 21457

35 55 5333 14423 14670 15438 19468 19667 20823 21084 21241 21344 21447 21520 21554 21586

13 20 2025 11854 12516 14938 15929 18081 19730 19929 20408 21338 21391 21425 21468 21546

54 7451 8176 10136 15240 16442 16482 19431 19483 19762 20647 20839 20966 21512 21579 21592

26 465 3604 4233 9831 11741 13692 18953 18974 21021 21039 21133 21282 21488 21532 21558

1 7 16 59 6979 7675 7717 9791 12370 13050 18534 18729 19846 19864 20127 20165

15 31 11089 12360 13640 14237 17937 18043 18410 19443 21107 21444 21449 21528 21576 21584

32 51 9768 17848 18095 19326 19594 19618 19765 20440 20482 20582 21236 21338 21563 21587

44 55 4864 10253 11306 12117 13076 13901 15610 17057 18205 19794 20939 21132 21267 21573

3436 11304 15361 16511 16860 18238 18639 19341 20106 20123 20407 21200 21280 21452 21526 21569

679 8822 11045 14403 16588 17838 19117 19453 20265 20558 21374 21396 21428 21442 21529 21590

391 13002 13140 14314 17169 17175 17846 18122 19447 20075 20212 20436 20583 21330 21359 21403

7601 10257 20060 21285

4419 9150 18097 20315

4675 13376 21435

610 1238 16704

5732 7096 21104

5690 13531 14545

4334 14839 17357

8 2814 17674

2392 8128 18369

502 7403 15133

343 13624 20673

13188 15687 21593

321 16866 21347

1242 4261 17449

4691 8086 8691

8500 11538 20278

6269 12905 18192

5984 15452 17111

11541 18717 21534

16 10780 16107

12310 12959 20390

1365 18306 19634

6125 19132 20242

3012 17233 21533

5816 13021 21440

13207 17811 18798

2762 7586 12139

3949 5545 13584

11374 18279 19241

2736 10989 21209

4095 20677 21395

8251 10084 20498

7628 8875 21406

2743 8943 9090

1817 7788 15767

9333 9838 21268

6203 9480 12042

5747 21187 21468

2553 18281 21500

3179 9155 15222

12498 18109 20326

14106 21209 21592

7454 17484 20791

20804 21120 21574

5754 18178 20935

30 4322 21381

11905 20416 21397

12452 19899 21497

1917 6028 16868

9891 18710 18953

912 21083 21446

370 14355 18069

16519 19003 20902

11163 17558 18424

8427 14396 21405

8885 11796 21361

4960 15431 20653

11944 16839 21236

9967 14529 17208

14144 19354 19745

7986 12680 21396

6097 11501 13028

33 13803 21038

3177 20124 20803

2692 6841 18655

971 5892 14354

3887 19455 21271

17214 17315 21148

6539 13910 21526

3809 5153 15793

3865 21438 21510

7129 17787 19636

5972 13150 14182

7078 14906 16911

15705 21160 21482

5479 13860 19763

16817 19722 20001

14649 16147 18886

15138 18578 21502

2096 2534 17760

11920 13460 19783

19876 20071 20583

6241 14230 20775

16138 16386 21371

8616 15624 18453

6013 8015 21599

9184 10688 20792

18122 21141 21469

10706 13177 20957

15148 15584 20959

9114 9432 16467

5483 14687 14705

8325 21161 21410

2328 17670 19834

7015 20802 21385

52 5451 20379

9689 15537 19733.

A seventh data processing apparatus or data processing method of the present technology includes an encoding unit configured to encode or an encoding step of encoding information bits into an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 21/30 on the basis of a parity check matrix of the LDPC code, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns, including

549 611 1357 3717 5079 5412 5964 10310 13716 16028 16067 16726 16856 18095 18515

25 163 1310 4468 5938 8348 9208 11118 13355 13539 14004 14869 16512 17878 19194

9 3271 4816 5091 5642 6704 8049 8431 8513 9264 10118 10905 17317 19047 19204

1775 2009 2741 3978 5427 6376 8143 9682 12173 13086 13232 14386 15220 17433 19332

18 519 4261 4265 6356 6409 11253 12973 14592 16637 17039 18474 19112 19202 19214

874 2918 3977 8791 9100 10391 10623 11738 16545 16968 17928 19049 19251 19295 19384

15 2832 4906 5010 7208 7315 8266 12524 14718 14789 16532 16637 17333 19314 19361

1 44 169 967 3980 7358 8489 9672 11731 12519 19027 19030 19156 19348 19434

32 112 2611 5885 6907 9231 9890 10047 10456 17955 17959 19236 19361 19395 19419

5 13 38 51 1307 6348 7275 10351 11869 13074 17179 17889 18802 18957 18963

45 1114 1822 13768 13968 16002 17945 18577 18944 19097 19142 19191 19211 19280 19410

16 25 31 6527 7318 10336 11522 11826 12038 17843 19218 19270 19346 19365 19428

44 3166 11719 13946 14592 16659 17881 18127 18335 18401 18672 19025 19093 19218 19233

3890 4804 10421 11575 15260 15641 15738 15835 16462 17085 17902 18650 19131 19328 19336

40 4635 6324 12215 13030 14029 15387 16287 18128 18893 18939 19138 19409 19416 19422

26 10421 10487 11386 12158 13231 16951 17521 18100 18309 18468 18689 18745 18862 19350

33 1635 8499 10728 12209 15641 16482 17298 18157 18247 18498 18885 19018 19304 19340

155 7584 9130 9253 10095 14414 15396 16572 16660 18942 19031 19287 19319 19334 19418

0 452 4180 6281 7401 13527 13855 14524 16190 18133 18346 18428 18983 19370 19377

43 5974 9711 10621 11296 13782 16955 17413 17514 17949 18441 18465 18800 19368 19380

20 2462 6141 6157 7855 13754 17444 17900 18517 19099 19217 19392 19416 19419 19436

44 3197 6827 8627 12967 13503 14327 15070 16306 17079 18212 18283 19000 19021 19318

0 9 24 784 875 2519 3900 5797 13090 13395 18070 18095 18767 19024 19212

27 1943 4688 5617 7512 7773 10220 13453 15976 15984 17284 17785 18950 19187 19422

2095 17203 18559

29 10616 15594

14366 14924 15179

5487 7882 14228

1228 19301 19420

2144 9744 10245

47 12037 16969

4990 8811 19259

13271 13624 18766

11793 15199 18405

13618 15135 16272

9174 15906 19070

10882 15172 19435

2925 5216 18611

8983 16271 19303

5729 11533 19203

3507 5159 11003

11001 13292 17253

101 1300 14833

8847 16410 19344

38 3941 11470

10236 12322 19338

1260 12919 18542

14 1600 18816

7291 10840 19376

13341 17748 18862

2024 16189 16472

15455 19239 19324

7128 12794 13415

2451 13218 15127

11 9927 15112

12 10965 18860

6608 9066 12275

41 18066 19438

9728 14238 15735

2681 18067 18373

5703 12695 17303

6313 10968 16782

11614 17966 19415

8655 11059 19328

5073 10392 17906

14548 18253 18669

19 14499 15650

2143 4832 19385

34 14211 19234

2 12953 17512

25 10861 17406

5130 5806 14134

39 7187 9438

10151 13443 14947

3133 17418 19306

10438 17365 18111

663 1871 9263

2263 10489 18872

1394 11495 14248

13142 14532 17626

4112 8384 17008

343 10678 16973

36 15014 18796

7493 9878 17251

4377 18986 19224

308 4759 14859

351 4223 15427

8202 9473 16372

34 11406 17412

288 17583 19377

11399 19314 19423

12751 16286 18472

8491 18395 19437

4963 17013 17320

8 8055 18734

16273 18187 18587

2518 11798 16676

53 10193 12952

12684 17095 19344

12177 17294 19409

2392 2779 11655

22 2710 13906

13632 18515 18736

7382 14797 19428

179 2268 14006

3906 17265 18591

7319 19149 19416

4758 6806 13737

5870 16687 18049

951 17955 18610

18594 19185 19230

12 10368 14750

9075 15399 16142

52 18271 19415

11188 16933 18251

5 3895 18928

42 4376 16217

392 10065 12992

24 6280 7491

5120 6017 14213

13487 18094 18488

6894 8901 18670

4309 7212 11581

4843 7906 17221

2422 10835 18516

26 16787 19383.

An eighth data processing apparatus or data processing method of the present technology includes a decoding unit configured to decode or a decoding step of decoding an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 21/30 on the basis of a parity check matrix of the LDPC code, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns, including

549 611 1357 3717 5079 5412 5964 10310 13716 16028 16067 16726 16856 18095 18515

25 163 1310 4468 5938 8348 9208 11118 13355 13539 14004 14869 16512 17878 19194

9 3271 4816 5091 5642 6704 8049 8431 8513 9264 10118 10905 17317 19047 19204

1775 2009 2741 3978 5427 6376 8143 9682 12173 13086 13232 14386 15220 17433 19332

18 519 4261 4265 6356 6409 11253 12973 14592 16637 17039 18474 19112 19202 19214

874 2918 3977 8791 9100 10391 10623 11738 16545 16968 17928 19049 19251 19295 19384

15 2832 4906 5010 7208 7315 8266 12524 14718 14789 16532 16637 17333 19314 19361

1 44 169 967 3980 7358 8489 9672 11731 12519 19027 19030 19156 19348 19434

32 112 2611 5885 6907 9231 9890 10047 10456 17955 17959 19236 19361 19395 19419

5 13 38 51 1307 6348 7275 10351 11869 13074 17179 17889 18802 18957 18963

45 1114 1822 13768 13968 16002 17945 18577 18944 19097 19142 19191 19211 19280 19410

16 25 31 6527 7318 10336 11522 11826 12038 17843 19218 19270 19346 19365 19428

44 3166 11719 13946 14592 16659 17881 18127 18335 18401 18672 19025 19093 19218 19233

3890 4804 10421 11575 15260 15641 15738 15835 16462 17085 17902 18650 19131 19328 19336

40 4635 6324 12215 13030 14029 15387 16287 18128 18893 18939 19138 19409 19416 19422

26 10421 10487 11386 12158 13231 16951 17521 18100 18309 18468 18689 18745 18862 19350

33 1635 8499 10728 12209 15641 16482 17298 18157 18247 18498 18885 19018 19304 19340

155 7584 9130 9253 10095 14414 15396 16572 16660 18942 19031 19287 19319 19334 19418

0 452 4180 6281 7401 13527 13855 14524 16190 18133 18346 18428 18983 19370 19377

43 5974 9711 10621 11296 13782 16955 17413 17514 17949 18441 18465 18800 19368 19380

20 2462 6141 6157 7855 13754 17444 17900 18517 19099 19217 19392 19416 19419 19436

44 3197 6827 8627 12967 13503 14327 15070 16306 17079 18212 18283 19000 19021 19318

0 9 24 784 875 2519 3900 5797 13090 13395 18070 18095 18767 19024 19212

27 1943 4688 5617 7512 7773 10220 13453 15976 15984 17284 17785 18950 19187 19422

2095 17203 18559

29 10616 15594

14366 14924 15179

5487 7882 14228

1228 19301 19420

2144 9744 10245

47 12037 16969

4990 8811 19259

13271 13624 18766

11793 15199 18405

13618 15135 16272

9174 15906 19070

10882 15172 19435

2925 5216 18611

8983 16271 19303

5729 11533 19203

3507 5159 11003

11001 13292 17253

101 1300 14833

8847 16410 19344

38 3941 11470

10236 12322 19338

1260 12919 18542

14 1600 18816

7291 10840 19376

13341 17748 18862

2024 16189 16472

15455 19239 19324

7128 12794 13415

2451 13218 15127

11 9927 15112

12 10965 18860

6608 9066 12275

41 18066 19438

9728 14238 15735

2681 18067 18373

5703 12695 17303

6313 10968 16782

11614 17966 19415

8655 11059 19328

5073 10392 17906

14548 18253 18669

19 14499 15650

2143 4832 19385

34 14211 19234

2 12953 17512

25 10861 17406

5130 5806 14134

39 7187 9438

10151 13443 14947

3133 17418 19306

10438 17365 18111

663 1871 9263

2263 10489 18872

1394 11495 14248

13142 14532 17626

4112 8384 17008

343 10678 16973

36 15014 18796

7493 9878 17251

4377 18986 19224

308 4759 14859

351 4223 15427

8202 9473 16372

34 11406 17412

288 17583 19377

11399 19314 19423

12751 16286 18472

8491 18395 19437

4963 17013 17320

8 8055 18734

16273 18187 18587

2518 11798 16676

53 10193 12952

12684 17095 19344

12177 17294 19409

2392 2779 11655

22 2710 13906

13632 18515 18736

7382 14797 19428

179 2268 14006

3906 17265 18591

7319 19149 19416

4758 6806 13737

5870 16687 18049

951 17955 18610

18594 19185 19230

12 10368 14750

9075 15399 16142

52 18271 19415

11188 16933 18251

5 3895 18928

42 4376 16217

392 10065 12992

24 6280 7491

5120 6017 14213

13487 18094 18488

6894 8901 18670

4309 7212 11581

4843 7906 17221

2422 10835 18516

26 16787 19383.

A ninth data processing apparatus or data processing method of the present technology includes an encoding unit configured to encode or an encoding step of encoding information bits into an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 22/30 on the basis of a parity check matrix of the LDPC code, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns, including

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 16456 16912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 16916 17137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 16714 17157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 17040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 17132 17226

1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 16024 16812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 15311 16391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 16961 17033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 16493 16690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 16616 16862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 17050 17060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 16799 16833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 17179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 16825 17112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 17102 17251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 15202 15335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 17103

40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 16274 17034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 17044 17250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 17177 17238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 17084 17193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255.

A tenth data processing apparatus or data processing method of the present technology includes a decoding unit configured to decode or a decoding step of decoding an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 22/30 on the basis of a parity check matrix of the LDPC code, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns, including

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 16456 16912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 16916 17137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 16714 17157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 17040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 17132 17226

1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 16024 16812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 15311 16391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 16961 17033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 16493 16690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 16616 16862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 17050 17060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 16799 16833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 17179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 16825 17112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 17102 17251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 15202 15335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 17103

40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 16274 17034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 17044 17250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 17177 17238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 17084 17193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255.

An eleventh data processing apparatus or data processing method of the present technology includes an encoding unit configured to encode or an encoding step of encoding information bits into an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 23/30 on the basis of a parity check matrix of the LDPC code, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns, including

310 1729 3466 4343 5079 5360 6486 7268 8660 8684 9687 10496 12682 13283 14142

10 35 3137 4489 4906 5614 6655 9072 10341 10512 11699 12547 12992 15098 15103

20 28 1671 4321 8051 8676 9003 10395 11047 11259 12221 13005 14041 14459 15078

82 329 2415 3798 8856 11071 11483 12210 12283 13592 14111 14118 14890 15043 15080

38 3425 4256 5892 6586 9088 10029 10168 10845 13170 13742 14143 14505 14648 14949

24 1462 5755 9371 9921 10303 11838 13574 13755 13982 14821 14848 14916 15082 15088

27 4818 7432 7508 8148 9725 10575 13009 13205 13469 14264 14707 14967 15029 15092

4118 6906 8252 10421 11578 12851 13114 13662 13815 14535 14795 14971 15007 15019 15094

34 5330 7799 9336 10563 11473 11624 13103 13490 13664 14286 14782 15013 15075 15089

30 1833 4359 7535 10347 10691 12403 13357 14063 14358 14554 14563 14611 14886 14894

2 11 2662 3363 5469 5674 8489 9870 11571 12625 14094 14602 14962 14972 15016

2666 3305 4681 8359 9701 9970 10838 11432 12869 13053 13873 14664 14703 14928 14998

3164 5920 5949 9228 10188 11757 12119 12878 13410 13951 14398 14652 14910 14967 15103

7840 9295 9875 11112 12316 12463 12771 13094 13197 13712 14085 14444 14707 14947 14987

1110 1223 3530 6281 10867 13008 14412 14528 14628 14753 14901 14938 15063 15087 15112

21 791 3863 5611 8101 10837 12988 13585 13731 14228 14435 14843 14910 15052 15082

40 1358 6434 9368 9892 10005 11561 11996 12506 13093 13167 14607 14674 14844 15030

803 1072 4593 6553 8291 8954 10035 11469 13719 14077 14173 14771 14812 14888 14992

6 5334 7322 7499 9560 10116 11560 11795 11874 11994 13936 14284 14376 14671 14863

41 5509 7768 9585 9698 10441 11621 12907 13092 13535 13832 14759 14887 14903 14972

4836 6794 8298 8883 10019 11625 12322 12563 13084 14192 14431 14526 14611 14883 15044

39 2210 7759 8572 8654 13258 13651 14070 14115 14279 14418 14566 14718 14811 15004

19 3975 4451 5642 6685 7975 8633 9640 9811 10753 10890 11243 11269 12598 14952

6363 6545 9439 9791 9818 13695 14229 14556 14711 14730 14744 14758 14844 14962 15032

6068 6472 6852 7431

3260 8709 11880 14644

8072 10635 12785 14902

936 12069 14934 14957

31 3503 7561 14443

4377 13028 14483 14513

397 6963 12232

8743 10726 14721

2800 3819 12560

11057 13202 15084

2256 4829 13796

2759 3104 14683

139 10014 12174

3531 9304 14860

3890 5170 13556

10401 13606 14910

4070 4564 7583

13749 14399 15019

2025 13882 15031

10616 11730 14148

2890 6342 12520

2071 6431 14496

8209 9125 13522

6008 7161 12442

14655 14792 15037

9054 14297 15119

5028 6219 12074

4932 6117 12187

12826 13557 14731

29 3332 10904

3244 5024 14841

1049 2209 13864

5834 7363 9300

8811 13949 15067

2676 14611 14917

4002 8661 14258

2371 3303 13028

3752 8981 15017

4942 10910 14170

3468 7594 8043

36 10685 12755

9662 11320 15033

9492 9545 15037

2896 12060 14451

702 9889 14014

645 2309 8254

4 10526 14294

24 6849 9207

4757 8294 14632

4831 14801 15043

10 6249 12881

4410 14983 15118

2286 7820 11208

7426 14880 14989

1509 10463 12060

1178 5443 8507

8631 9398 13789

6338 14601 15113

7697 10138 15054

3320 4956 8415

3367 13345 14874

13 2297 12215

610 10921 13983

7774 9106 13675

14 6002 6695

10257 13816 15090

12630 13922 14694

11114 14476 15105

32 9315 14962

5 3297 5106

3295 5972 10033

2417 14325 14447

2402 13380 13428

18 3172 14813

25 2268 9077

8145 8832 9014

2603 12606 12669

28 6315 14074

2569 3887 13526

2849 4358 15087

4385 7371 15088

6751 9658 13980

2701 4780 14869

625 3867 4178

11687 13958 14425

5036 12280 14985

3 9966 15042

16 14222 14721

1847 14627 14856

3933 4622 7832

29 4886 14278

1436 4839 7869

1504 11063 14943

8386 11749 15046

9371 10290 13903

9762 10901 15068

4162 8497 9405

7 22 8605

1547 9194 15102

6997 12409 14946

2680 7168 15066

3835 11767 13355

68 11375 13564

2404 11541 14983

5828 11258 14013

50 611 14485

8228 13664 14202

2397 7302 14977

9954 13847 14514

1733 13749 15058

173 13024 14763

12 7767 15052

4429 12945 14972

9425 15079 15096.

A twelfth data processing apparatus or data processing method of the present technology includes a decoding unit configured to decode or a decoding step of decoding an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 23/30 on the basis of a parity check matrix of the LDPC code, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns, including

310 1729 3466 4343 5079 5360 6486 7268 8660 8684 9687 10496 12682 13283 14142

10 35 3137 4489 4906 5614 6655 9072 10341 10512 11699 12547 12992 15098 15103

20 28 1671 4321 8051 8676 9003 10395 11047 11259 12221 13005 14041 14459 15078

82 329 2415 3798 8856 11071 11483 12210 12283 13592 14111 14118 14890 15043 15080

38 3425 4256 5892 6586 9088 10029 10168 10845 13170 13742 14143 14505 14648 14949

24 1462 5755 9371 9921 10303 11838 13574 13755 13982 14821 14848 14916 15082 15088

27 4818 7432 7508 8148 9725 10575 13009 13205 13469 14264 14707 14967 15029 15092

4118 6906 8252 10421 11578 12851 13114 13662 13815 14535 14795 14971 15007 15019 15094

34 5330 7799 9336 10563 11473 11624 13103 13490 13664 14286 14782 15013 15075 15089

30 1833 4359 7535 10347 10691 12403 13357 14063 14358 14554 14563 14611 14886 14894

2 11 2662 3363 5469 5674 8489 9870 11571 12625 14094 14602 14962 14972 15016

2666 3305 4681 8359 9701 9970 10838 11432 12869 13053 13873 14664 14703 14928 14998

3164 5920 5949 9228 10188 11757 12119 12878 13410 13951 14398 14652 14910 14967 15103

7840 9295 9875 11112 12316 12463 12771 13094 13197 13712 14085 14444 14707 14947 14987

1110 1223 3530 6281 10867 13008 14412 14528 14628 14753 14901 14938 15063 15087 15112

21 791 3863 5611 8101 10837 12988 13585 13731 14228 14435 14843 14910 15052 15082

40 1358 6434 9368 9892 10005 11561 11996 12506 13093 13167 14607 14674 14844 15030

803 1072 4593 6553 8291 8954 10035 11469 13719 14077 14173 14771 14812 14888 14992

6 5334 7322 7499 9560 10116 11560 11795 11874 11994 13936 14284 14376 14671 14863

41 5509 7768 9585 9698 10441 11621 12907 13092 13535 13832 14759 14887 14903 14972

4836 6794 8298 8883 10019 11625 12322 12563 13084 14192 14431 14526 14611 14883 15044

39 2210 7759 8572 8654 13258 13651 14070 14115 14279 14418 14566 14718 14811 15004

19 3975 4451 5642 6685 7975 8633 9640 9811 10753 10890 11243 11269 12598 14952

6363 6545 9439 9791 9818 13695 14229 14556 14711 14730 14744 14758 14844 14962 15032

6068 6472 6852 7431

3260 8709 11880 14644

8072 10635 12785 14902

936 12069 14934 14957

31 3503 7561 14443

4377 13028 14483 14513

397 6963 12232

8743 10726 14721

2800 3819 12560

11057 13202 15084

2256 4829 13796

2759 3104 14683

139 10014 12174

3531 9304 14860

3890 5170 13556

10401 13606 14910

4070 4564 7583

13749 14399 15019

2025 13882 15031

10616 11730 14148

2890 6342 12520

2071 6431 14496

8209 9125 13522

6008 7161 12442

14655 14792 15037

9054 14297 15119

5028 6219 12074

4932 6117 12187

12826 13557 14731

29 3332 10904

3244 5024 14841

1049 2209 13864

5834 7363 9300

8811 13949 15067

2676 14611 14917

4002 8661 14258

2371 3303 13028

3752 8981 15017

4942 10910 14170

3468 7594 8043

36 10685 12755

9662 11320 15033

9492 9545 15037

2896 12060 14451

702 9889 14014

645 2309 8254

4 10526 14294

24 6849 9207

4757 8294 14632

4831 14801 15043

10 6249 12881

4410 14983 15118

2286 7820 11208

7426 14880 14989

1509 10463 12060

1178 5443 8507

8631 9398 13789

6338 14601 15113

7697 10138 15054

3320 4956 8415

3367 13345 14874

13 2297 12215

610 10921 13983

7774 9106 13675

14 6002 6695

10257 13816 15090

12630 13922 14694

11114 14476 15105

32 9315 14962

5 3297 5106

3295 5972 10033

2417 14325 14447

2402 13380 13428

18 3172 14813

25 2268 9077

8145 8832 9014

2603 12606 12669

28 6315 14074

2569 3887 13526

2849 4358 15087

4385 7371 15088

6751 9658 13980

2701 4780 14869

625 3867 4178

11687 13958 14425

5036 12280 14985

3 9966 15042

16 14222 14721

1847 14627 14856

3933 4622 7832

29 4886 14278

1436 4839 7869

1504 11063 14943

8386 11749 15046

9371 10290 13903

9762 10901 15068

4162 8497 9405

7 22 8605

1547 9194 15102

6997 12409 14946

2680 7168 15066

3835 11767 13355

68 11375 13564

2404 11541 14983

5828 11258 14013

50 611 14485

8228 13664 14202

2397 7302 14977

9954 13847 14514

1733 13749 15058

173 13024 14763

12 7767 15052

4429 12945 14972

9425 15079 15096.

In the present technology, information bits are encoded into an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 18/30, 19/30, 20/30, 21/30, 22/30, or 23/30 on the basis of a parity check matrix of the LDPC code.

In the present technology, furthermore, an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 18/30, 19/30, 20/30, 21/30, 22/30, or 23/30 is decoded on the basis of the parity check matrix of an LDPC code.

The LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns.

A parity check matrix initial value table with a code rate of 18/30 includes

113 1557 3316 5680 6241 10407 13404 13947 14040 14353 15522 15698 16079 17363 19374 19543 20530 22833 24339

271 1361 6236 7006 7307 7333 12768 15441 15568 17923 18341 20321 21502 22023 23938 25351 25590 25876 25910

73 605 872 4008 6279 7653 10346 10799 12482 12935 13604 15909 16526 19782 20506 22804 23629 24859 25600

1445 1690 4304 4851 8919 9176 9252 13783 16076 16675 17274 18806 18882 20819 21958 22451 23869 23999 24177

1290 2337 5661 6371 8996 10102 10941 11360 12242 14918 16808 20571 23374 24046 25045 25060 25662 25783 25913

28 42 1926 3421 3503 8558 9453 10168 15820 17473 19571 19685 22790 23336 23367 23890 24061 25657 25680

0 1709 4041 4932 5968 7123 8430 9564 10596 11026 14761 19484 20762 20858 23803 24016 24795 25853 25863

29 1625 6500 6609 16831 18517 18568 18738 19387 20159 20544 21603 21941 24137 24269 24416 24803 25154 25395

55 66 871 3700 11426 13221 15001 16367 17601 18380 22796 23488 23938 25476 25635 25678 25807 25857 25872

1 19 5958 8548 8860 11489 16845 18450 18469 19496 20190 23173 25262 25566 25668 25679 25858 25888 25915

7520 7690 8855 9183 14654 16695 17121 17854 18083 18428 19633 20470 20736 21720 22335 23273 25083 25293 25403

48 58 410 1299 3786 10668 18523 18963 20864 22106 22308 23033 23107 23128 23990 24286 24409 24595 25802

12 51 3894 6539 8276 10885 11644 12777 13427 14039 15954 17078 19053 20537 22863 24521 25087 25463 25838

3509 8748 9581 11509 15884 16230 17583 19264 20900 21001 21310 22547 22756 22959 24768 24814 25594 25626 25880

21 29 69 1448 2386 4601 6626 6667 10242 13141 13852 14137 18640 19951 22449 23454 24431 25512 25814

18 53 7890 9934 10063 16728 19040 19809 20825 21522 21800 23582 24556 25031 25547 25562 25733 25789 25906

4096 4582 5766 5894 6517 10027 12182 13247 15207 17041 18958 20133 20503 22228 24332 24613 25689 25855 25883

0 25 819 5539 7076 7536 7695 9532 13668 15051 17683 19665 20253 21996 24136 24890 25758 25784 25807

34 40 44 4215 6076 7427 7965 8777 11017 15593 19542 22202 22973 23397 23423 24418 24873 25107 25644

1595 6216 22850 25439

1562 15172 19517 22362

7508 12879 24324 24496

6298 15819 16757 18721

11173 15175 19966 21195

59 13505 16941 23793

2267 4830 12023 20587

8827 9278 13072 16664

14419 17463 23398 25348

6112 16534 20423 22698

493 8914 21103 24799

6896 12761 13206 25873

2 1380 12322 21701

11600 21306 25753 25790

8421 13076 14271 15401

9630 14112 19017 20955

212 13932 21781 25824

5961 9110 16654 19636

58 5434 9936 12770

6575 11433 19798

2731 7338 20926

14253 18463 25404

21791 24805 25869

2 11646 15850

6075 8586 23819

18435 22093 24852

2103 2368 11704

10925 17402 18232

9062 25061 25674

18497 20853 23404

18606 19364 19551

7 1022 25543

6744 15481 25868

9081 17305 25164

8 23701 25883

9680 19955 22848

56 4564 19121

5595 15086 25892

3174 17127 23183

19397 19817 20275

12561 24571 25825

7111 9889 25865

19104 20189 21851

549 9686 25548

6586 20325 25906

3224 20710 21637

641 15215 25754

13484 23729 25818

2043 7493 24246

16860 25230 25768

22047 24200 24902

9391 18040 19499

7855 24336 25069

23834 25570 25852

1977 8800 25756

6671 21772 25859

3279 6710 24444

24099 25117 25820

5553 12306 25915

48 11107 23907

10832 11974 25773

2223 17905 25484

16782 17135 20446

475 2861 3457

16218 22449 24362

11716 22200 25897

8315 15009 22633

13 20480 25852

12352 18658 25687

3681 14794 23703

30 24531 25846

4103 22077 24107

23837 25622 25812

3627 13387 25839

908 5367 19388

0 6894 25795

20322 23546 25181

8178 25260 25437

2449 13244 22565

31 18928 22741

1312 5134 14838

6085 13937 24220

66 14633 25670

47 22512 25472

8867 24704 25279

6742 21623 22745

147 9948 24178

8522 24261 24307

19202 22406 24609.

A parity check matrix initial value table with a code rate of 19/30 includes

354 794 1214 1640 8278 9195 11069 11580 11911 13276 13438 14495 14734 15741 19195 19537 21951

4657 5351 5887 6634 7718 8327 10300 10815 11822 13506 16746 19429 19920 21548 22087 23650 23712

4603 5160 6345 7259 8428 8937 9665 11623 11864 13590 13613 17117 18678 19118 21126 21884 23054

27 2157 3039 3219 4191 5651 7098 12555 12634 13791 14885 15505 16163 16664 19792 20437 23588

30 49 2768 3314 4345 6972 8994 15294 16653 18282 18808 19324 20597 21510 21643 23741 23748

1 553 2228 4277 4499 5818 10580 10823 12135 14102 14923 15980 15995 16319 18577 22838 23058

4 2307 2764 3075 4755 8064 9673 12150 21139 21224 21572 21682 23415 23598 23703 23710 23739

4 9 13 5867 6028 7730 10859 14755 14879 15746 21166 21643 22777 23409 23502 23511 23734

13 28 481 7146 8144 13768 15081 19349 20187 20858 21913 22025 23134 23472 23506 23711 23744

12 24 36 1004 3080 3496 7356 7834 16011 16492 19536 20918 22833 22937 23717 23745 23749

31 378 812 1578 1957 5163 14759 16701 16829 18111 22931 23253 23314 23351 23584 23660 23699

25 38 1183 6573 9556 12523 14303 14412 18209 18530 21334 21770 21809 22630 22734 23154 23186

57 3497 6667 9653 10168 12771 15082 19365 19415 19514 19611 19785 21242 22974 23107 23690 23715

2456 2562 6223 7150 12652 14580 14807 20072 20513 21091 21201 21922 23010 23046 23215 23514 23663

5 635 3760 4981 6824 8425 13532 14618 19654 20026 21439 21684 22023 23027 23499 23691 23707

8 3018 4509 9002 11537 17156 17490 17779 20182 22018 22416 23348 23497 23575 23685 23708 23753

3 19 60 9502 12512 12907 17118 20225 20508 21429 21695 22010 22187 22347 23574 23608 23617

2 5 22 61 6583 15302 17930 18081 18562 19427 21204 21744 22713 23422 23503 23597 23730

15 4333 9774 11921 15075 20998 21581 21622 22468 22638 23104 23530 23593 23613 23645 23648 23719

16 48 65 2563 3079 12594 17391 17524 20302 21062 21809 22772 23189

23501 23625 23628 23756

59 4288 6124 13237 13580 13607 19899 20348 21481 22380 22510 22883 23114 23233 23709 23715 23735

46 2949 3278 6100 9887 10255 19509 19883 20022 21147 21422 21915 22489 22777 23422 23750 23754

761 8196 8895 23472

10842 15470 23658 23748

13 16585 19888 21445

13341 17522 18603 20826

2932 8194 19093 21220

6202 9623 23715

2288 21290 22116

5143 10529 19731

15559 16069 23704

137 11927 20849

11 5997 11214

1212 9635 22820

8785 10770 15217

14930 15004 19622

15 9351 22137

6984 10545 18086

17 5394 22378

5666 17493 23525

2788 2962 18427

15308 18638 23694

6477 21407 23683

5907 22795 23101

3398 17256 18334

3010 12780 18130

2912 12048 19907

10071 21798 22747

9806 23050 23683

13541 23317 23733

11998 12007 17363

9401 16372 23473

16221 19981 21929

32 7499 20187

17718 22377 23147

17276 21344 22014

21779 22541 23607

16248 18722 23096

4225 19889 20582

21394 23463 23652

10428 11323 12984

60 23098 23752

8941 12692 20396

3909 12976 23323

4172 13704 21088

4252 20334 23229

5669 9953 23616

747 22117 23391

1201 17300 19083

6226 22684 23382

8854 14713 23706

18391 19269 20334

15856 16811 23747

39 3964 14259

11159 17884 18130

11388 23637 23738

12481 16865 23422

17762 22000 23602

13515 19709 21596

45 16207 16302

2011 13753 23611

20451 23564 23756

13 10379 16323

20 14421 16684

11082 19565 22082

9158 9437 20186

9270 21333 22631

24 22736 23382

28 19129 21403

34 1541 19415

18638 22335 23418

42 8892 23629

13154 13353 22663

51 2780 21921

45 6677 20895

61 15836 22536

15246 23565 23578

48 22661 23012

17 21419 23698

22650 23448 23497

20671 22579 23692

27 7302 23401

9478 19287 20789

9312 23176 23598

3566 21768 23652

19 6707 11777

430 19822 22687

1705 6631 23312

5 19562 23680

644 2620 13917

3998 22493 23529

20916 22930 23741

12467 22100 23737

8546 15903 22828.

A parity check matrix initial value table with a code rate of 20/30 includes

692 1779 1973 2726 5151 6088 7921 9618 11804 13043 15975 16214 16889 16980 18585 18648

13 4090 4319 5288 8102 10110 10481 10527 10953 11185 12069 13177 14217 15963 17661 20959

2330 2516 2902 4087 6338 8015 8638 9436 10294 10843 11802 12304 12371 14095 18486 18996

125 586 5137 5701 6432 6500 8131 8327 10488 11032 11334 11449 12504 16000 20753 21317

30 480 2681 3635 3898 4058 12803 14734 20252 20306 20680 21329 21333 21466 21562 21568

20 44 738 4965 5516 7659 8464 8759 12216 14630 18241 18711 19093 20217 21316 21490

31 43 3554 5289 5667 8687 14885 16579 17883 18384 18486 19142 20785 20932 21131 21308

7054 9276 10435 12324 12354 13849 14285 16482 19212 19217 19221 20499 20831 20925 21195 21247

9 13 4099 10353 10747 14884 15492 17650 19291 19394 20356 20658 21068 21117 21183 21586

28 2250 2980 8988 10282 12503 13301 18351 20546 20622 21006 21293 21344 21472 21530 21542

17 32 2521 4374 5098 7525 13035 14437 15283 18635 19136 20240 21147 21179 21300 21349

57 4735 5657 7649 8807 12375 16092 16178 16379 17545 19461 19489 20321 20530 21453 21457

35 55 5333 14423 14670 15438 19468 19667 20823 21084 21241 21344 21447 21520 21554 21586

13 20 2025 11854 12516 14938 15929 18081 19730 19929 20408 21338 21391 21425 21468 21546

54 7451 8176 10136 15240 16442 16482 19431 19483 19762 20647 20839 20966 21512 21579 21592

26 465 3604 4233 9831 11741 13692 18953 18974 21021 21039 21133 21282 21488 21532 21558

1 7 16 59 6979 7675 7717 9791 12370 13050 18534 18729 19846 19864 20127 20165

15 31 11089 12360 13640 14237 17937 18043 18410 19443 21107 21444 21449 21528 21576 21584

32 51 9768 17848 18095 19326 19594 19618 19765 20440 20482 20582 21236 21338 21563 21587

44 55 4864 10253 11306 12117 13076 13901 15610 17057 18205 19794 20939 21132 21267 21573

3436 11304 15361 16511 16860 18238 18639 19341 20106 20123 20407 21200 21280 21452 21526 21569

679 8822 11045 14403 16588 17838 19117 19453 20265 20558 21374 21396 21428 21442 21529 21590

391 13002 13140 14314 17169 17175 17846 18122 19447 20075 20212 20436 20583 21330 21359 21403

7601 10257 20060 21285

4419 9150 18097 20315

4675 13376 21435

610 1238 16704

5732 7096 21104

5690 13531 14545

4334 14839 17357

8 2814 17674

2392 8128 18369

502 7403 15133

343 13624 20673

13188 15687 21593

321 16866 21347

1242 4261 17449

4691 8086 8691

8500 11538 20278

6269 12905 18192

5984 15452 17111

11541 18717 21534

16 10780 16107

12310 12959 20390

1365 18306 19634

6125 19132 20242

3012 17233 21533

5816 13021 21440

13207 17811 18798

2762 7586 12139

3949 5545 13584

11374 18279 19241

2736 10989 21209

4095 20677 21395

8251 10084 20498

7628 8875 21406

2743 8943 9090

1817 7788 15767

9333 9838 21268

6203 9480 12042

5747 21187 21468

2553 18281 21500

3179 9155 15222

12498 18109 20326

14106 21209 21592

7454 17484 20791

20804 21120 21574

5754 18178 20935

30 4322 21381

11905 20416 21397

12452 19899 21497

1917 6028 16868

9891 18710 18953

912 21083 21446

370 14355 18069

16519 19003 20902

11163 17558 18424

8427 14396 21405

8885 11796 21361

4960 15431 20653

11944 16839 21236

9967 14529 17208

14144 19354 19745

7986 12680 21396

6097 11501 13028

33 13803 21038

3177 20124 20803

2692 6841 18655

971 5892 14354

3887 19455 21271

17214 17315 21148

6539 13910 21526

3809 5153 15793

3865 21438 21510

7129 17787 19636

5972 13150 14182

7078 14906 16911

15705 21160 21482

5479 13860 19763

16817 19722 20001

14649 16147 18886

15138 18578 21502

2096 2534 17760

11920 13460 19783

19876 20071 20583

6241 14230 20775

16138 16386 21371

8616 15624 18453

6013 8015 21599

9184 10688 20792

18122 21141 21469

10706 13177 20957

15148 15584 20959

9114 9432 16467

5483 14687 14705

8325 21161 21410

2328 17670 19834

7015 20802 21385

52 5451 20379

9689 15537 19733.

A parity check matrix initial value table with a code rate of 21/30 includes

549 611 1357 3717 5079 5412 5964 10310 13716 16028 16067 16726 16856 18095 18515

25 163 1310 4468 5938 8348 9208 11118 13355 13539 14004 14869 16512 17878 19194

9 3271 4816 5091 5642 6704 8049 8431 8513 9264 10118 10905 17317 19047 19204

1775 2009 2741 3978 5427 6376 8143 9682 12173 13086 13232 14386 15220 17433 19332

18 519 4261 4265 6356 6409 11253 12973 14592 16637 17039 18474 19112 19202 19214

874 2918 3977 8791 9100 10391 10623 11738 16545 16968 17928 19049 19251 19295 19384

15 2832 4906 5010 7208 7315 8266 12524 14718 14789 16532 16637 17333 19314 19361

1 44 169 967 3980 7358 8489 9672 11731 12519 19027 19030 19156 19348 19434

32 112 2611 5885 6907 9231 9890 10047 10456 17955 17959 19236 19361 19395 19419

5 13 38 51 1307 6348 7275 10351 11869 13074 17179 17889 18802 18957 18963

45 1114 1822 13768 13968 16002 17945 18577 18944 19097 19142 19191 19211 19280 19410

16 25 31 6527 7318 10336 11522 11826 12038 17843 19218 19270 19346 19365 19428

44 3166 11719 13946 14592 16659 17881 18127 18335 18401 18672 19025 19093 19218 19233

3890 4804 10421 11575 15260 15641 15738 15835 16462 17085 17902 18650 19131 19328 19336

40 4635 6324 12215 13030 14029 15387 16287 18128 18893 18939 19138 19409 19416 19422

26 10421 10487 11386 12158 13231 16951 17521 18100 18309 18468 18689 18745 18862 19350

33 1635 8499 10728 12209 15641 16482 17298 18157 18247 18498 18885 19018 19304 19340

155 7584 9130 9253 10095 14414 15396 16572 16660 18942 19031 19287 19319 19334 19418

0 452 4180 6281 7401 13527 13855 14524 16190 18133 18346 18428 18983 19370 19377

43 5974 9711 10621 11296 13782 16955 17413 17514 17949 18441 18465 18800 19368 19380

20 2462 6141 6157 7855 13754 17444 17900 18517 19099 19217 19392 19416 19419 19436

44 3197 6827 8627 12967 13503 14327 15070 16306 17079 18212 18283 19000 19021 19318

0 9 24 784 875 2519 3900 5797 13090 13395 18070 18095 18767 19024 19212

27 1943 4688 5617 7512 7773 10220 13453 15976 15984 17284 17785 18950 19187 19422

2095 17203 18559

29 10616 15594

14366 14924 15179

5487 7882 14228

1228 19301 19420

2144 9744 10245

47 12037 16969

4990 8811 19259

13271 13624 18766

11793 15199 18405

13618 15135 16272

9174 15906 19070

10882 15172 19435

2925 5216 18611

8983 16271 19303

5729 11533 19203

3507 5159 11003

11001 13292 17253

101 1300 14833

8847 16410 19344

38 3941 11470

10236 12322 19338

1260 12919 18542

14 1600 18816

7291 10840 19376

13341 17748 18862

2024 16189 16472

15455 19239 19324

7128 12794 13415

2451 13218 15127

11 9927 15112

12 10965 18860

6608 9066 12275

41 18066 19438

9728 14238 15735

2681 18067 18373

5703 12695 17303

6313 10968 16782

11614 17966 19415

8655 11059 19328

5073 10392 17906

14548 18253 18669

19 14499 15650

2143 4832 19385

34 14211 19234

2 12953 17512

25 10861 17406

5130 5806 14134

39 7187 9438

10151 13443 14947

3133 17418 19306

10438 17365 18111

663 1871 9263

2263 10489 18872

1394 11495 14248

13142 14532 17626

4112 8384 17008

343 10678 16973

36 15014 18796

7493 9878 17251

4377 18986 19224

308 4759 14859

351 4223 15427

8202 9473 16372

34 11406 17412

288 17583 19377

11399 19314 19423

12751 16286 18472

8491 18395 19437

4963 17013 17320

8 8055 18734

16273 18187 18587

2518 11798 16676

53 10193 12952

12684 17095 19344

12177 17294 19409

2392 2779 11655

22 2710 13906

13632 18515 18736

7382 14797 19428

179 2268 14006

3906 17265 18591

7319 19149 19416

4758 6806 13737

5870 16687 18049

951 17955 18610

18594 19185 19230

12 10368 14750

9075 15399 16142

52 18271 19415

11188 16933 18251

5 3895 18928

42 4376 16217

392 10065 12992

24 6280 7491

5120 6017 14213

13487 18094 18488

6894 8901 18670

4309 7212 11581

4843 7906 17221

2422 10835 18516

26 16787 19383.

A parity check matrix initial value table with a code rate of 22/30 includes

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 16456 16912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 16916 17137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 16714 17157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 17040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 17132 17226

1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 16024 16812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 15311 16391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 16961 17033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 16493 16690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 16616 16862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 17050 17060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 16799 16833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 17179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 16825 17112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 17102 17251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 15202 15335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 17103

40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 16274 17034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 17044 17250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 17177 17238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 17084 17193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255.

A parity check matrix initial value table with a code rate of 23/30 includes

310 1729 3466 4343 5079 5360 6486 7268 8660 8684 9687 10496 12682 13283 14142

10 35 3137 4489 4906 5614 6655 9072 10341 10512 11699 12547 12992 15098 15103

20 28 1671 4321 8051 8676 9003 10395 11047 11259 12221 13005 14041 14459 15078

82 329 2415 3798 8856 11071 11483 12210 12283 13592 14111 14118 14890 15043 15080

38 3425 4256 5892 6586 9088 10029 10168 10845 13170 13742 14143 14505 14648 14949

24 1462 5755 9371 9921 10303 11838 13574 13755 13982 14821 14848 14916 15082 15088

27 4818 7432 7508 8148 9725 10575 13009 13205 13469 14264 14707 14967 15029 15092

4118 6906 8252 10421 11578 12851 13114 13662 13815 14535 14795 14971 15007 15019 15094

34 5330 7799 9336 10563 11473 11624 13103 13490 13664 14286 14782 15013 15075 15089

30 1833 4359 7535 10347 10691 12403 13357 14063 14358 14554 14563 14611 14886 14894

2 11 2662 3363 5469 5674 8489 9870 11571 12625 14094 14602 14962 14972 15016

2666 3305 4681 8359 9701 9970 10838 11432 12869 13053 13873 14664 14703 14928 14998

3164 5920 5949 9228 10188 11757 12119 12878 13410 13951 14398 14652 14910 14967 15103

7840 9295 9875 11112 12316 12463 12771 13094 13197 13712 14085 14444 14707 14947 14987

1110 1223 3530 6281 10867 13008 14412 14528 14628 14753 14901 14938 15063 15087 15112

21 791 3863 5611 8101 10837 12988 13585 13731 14228 14435 14843 14910 15052 15082

40 1358 6434 9368 9892 10005 11561 11996 12506 13093 13167 14607 14674 14844 15030

803 1072 4593 6553 8291 8954 10035 11469 13719 14077 14173 14771 14812 14888 14992

6 5334 7322 7499 9560 10116 11560 11795 11874 11994 13936 14284 14376 14671 14863

41 5509 7768 9585 9698 10441 11621 12907 13092 13535 13832 14759 14887 14903 14972

4836 6794 8298 8883 10019 11625 12322 12563 13084 14192 14431 14526 14611 14883 15044

39 2210 7759 8572 8654 13258 13651 14070 14115 14279 14418 14566 14718 14811 15004

19 3975 4451 5642 6685 7975 8633 9640 9811 10753 10890 11243 11269 12598 14952

6363 6545 9439 9791 9818 13695 14229 14556 14711 14730 14744 14758 14844 14962 15032

6068 6472 6852 7431

3260 8709 11880 14644

8072 10635 12785 14902

936 12069 14934 14957

31 3503 7561 14443

4377 13028 14483 14513

397 6963 12232

8743 10726 14721

2800 3819 12560

11057 13202 15084

2256 4829 13796

2759 3104 14683

139 10014 12174

3531 9304 14860

3890 5170 13556

10401 13606 14910

4070 4564 7583

13749 14399 15019

2025 13882 15031

10616 11730 14148

2890 6342 12520

2071 6431 14496

8209 9125 13522

6008 7161 12442

14655 14792 15037

9054 14297 15119

5028 6219 12074

4932 6117 12187

12826 13557 14731

29 3332 10904

3244 5024 14841

1049 2209 13864

5834 7363 9300

8811 13949 15067

2676 14611 14917

4002 8661 14258

2371 3303 13028

3752 8981 15017

4942 10910 14170

3468 7594 8043

36 10685 12755

9662 11320 15033

9492 9545 15037

2896 12060 14451

702 9889 14014

645 2309 8254

4 10526 14294

24 6849 9207

4757 8294 14632

4831 14801 15043

10 6249 12881

4410 14983 15118

2286 7820 11208

7426 14880 14989

1509 10463 12060

1178 5443 8507

8631 9398 13789

6338 14601 15113

7697 10138 15054

3320 4956 8415

3367 13345 14874

13 2297 12215

610 10921 13983

7774 9106 13675

14 6002 6695

10257 13816 15090

12630 13922 14694

11114 14476 15105

32 9315 14962

5 3297 5106

3295 5972 10033

2417 14325 14447

2402 13380 13428

18 3172 14813

25 2268 9077

8145 8832 9014

2603 12606 12669

28 6315 14074

2569 3887 13526

2849 4358 15087

4385 7371 15088

6751 9658 13980

2701 4780 14869

625 3867 4178

11687 13958 14425

5036 12280 14985

3 9966 15042

16 14222 14721

1847 14627 14856

3933 4622 7832

29 4886 14278

1436 4839 7869

1504 11063 14943

8386 11749 15046

9371 10290 13903

9762 10901 15068

4162 8497 9405

7 22 8605

1547 9194 15102

6997 12409 14946

2680 7168 15066

3835 11767 13355

68 11375 13564

2404 11541 14983

5828 11258 14013

50 611 14485

8228 13664 14202

2397 7302 14977

9954 13847 14514

1733 13749 15058

173 13024 14763

12 7767 15052

4429 12945 14972

9425 15079 15096.

Note that each data processing apparatus may be an independent apparatus, or may be an internal block in a single apparatus.

Advantageous Effects of Invention

According to the present technology, it is possible to provide LDPC codes having good error-rate performance.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram depicting a parity check matrix H of an LDPC code.

FIG. 2 is a flowchart depicting an LDPC code decoding procedure.

FIG. 3 is a diagram illustrating an example of a parity check matrix of an LDPC code.

FIG. 4 is a diagram illustrating a Tanner graph of a parity check matrix.

FIG. 5 is a diagram illustrating a variable node.

FIG. 6 is a diagram illustrating a check node.

FIG. 7 is a diagram illustrating an example configuration of an embodiment of a transmission system to which the present technology applies.

FIG. 8 is a block diagram illustrating an example configuration of a transmitting device 11.

FIG. 9 is a block diagram illustrating an example configuration of a bit interleaver 116.

FIG. 10 is a diagram illustrating a parity check matrix.

FIG. 11 is a diagram illustrating a parity matrix.

FIG. 12 is a diagram depicting a parity check matrix of an LDPC code defined in the DVB-S.2 standard.

FIG. 13 is a diagram depicting a parity check matrix of an LDPC code defined in the DVB-S.2 standard.

FIG. 14 includes diagrams illustrating an arrangement of constellation points of 16QAM.

FIG. 15 is a diagram illustrating arrangements of constellation points of 64QAM.

FIG. 16 is a diagram illustrating arrangements of constellation points of 64QAM.

FIG. 17 is a diagram illustrating arrangements of constellation points of 64QAM.

FIG. 18 is a diagram illustrating an arrangement of constellation points defined in the DVB-S.2 standard.

FIG. 19 is a diagram illustrating an arrangement of constellation points defined in the DVB-S.2 standard.

FIG. 20 includes diagrams illustrating an arrangement of constellation points defined in the DVB-S.2 standard.

FIG. 21 includes diagrams illustrating an arrangement of constellation points defined in the DVB-S.2 standard.

FIG. 22 includes diagrams depicting the processing of a demultiplexer 25.

FIG. 23 includes diagrams depicting the processing of the demultiplexer 25.

FIG. 24 is a diagram illustrating a Tanner graph for LDPC code decoding.

FIG. 25 includes diagrams illustrating a parity matrix H_(T) having a stepwise structure, and a Tanner graph corresponding to the parity matrix H_(T).

FIG. 26 is a diagram illustrating a parity matrix H_(T) of a parity check matrix H corresponding to an LDPC code that has been subjected to parity interleaving.

FIG. 27 includes diagrams illustrating a transformed parity check matrix.

FIG. 28 is a diagram depicting the processing of a column twist interleaver 24.

FIG. 29 is a diagram illustrating the numbers of columns of a memory 31 which are necessary for column twist interleaving, and the addresses of write start positions.

FIG. 30 is a diagram illustrating the numbers of columns of the memory 31 which are necessary for column twist interleaving, and the addresses of write start positions.

FIG. 31 is a flowchart depicting a process performed by the bit interleaver 116 and a QAM encoder 117.

FIG. 32 includes diagrams illustrating a model of a communication path used in simulations.

FIG. 33 is a diagram illustrating relationships between Doppler frequencies f_(d) of flutters and error rates obtained in simulations.

FIG. 34 is a diagram illustrating relationships between Doppler frequencies f_(d) of flutters and error rates obtained in the simulations.

FIG. 35 is a block diagram illustrating an example configuration of an LDPC encoder 115.

FIG. 36 is a flowchart depicting a process of the LDPC encoder 115.

FIG. 37 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 1/4 and the code length 16200.

FIG. 38 is a diagram depicting a method for determining a parity check matrix H from a parity check matrix initial value table.

FIG. 39 is a diagram illustrating the BER/FER characteristics of an LDPC code having a code length of 64800 bits, which is defined in the DVB-S.2 standard.

FIG. 40 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 2/30 and the code length 64800.

FIG. 41 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 3/30 and the code length 64800.

FIG. 42 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 4/30 and the code length 64800.

FIG. 43 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 5/30 and the code length 64800.

FIG. 44 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 6/30 and the code length 64800.

FIG. 45 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 7/30 and the code length 64800.

FIG. 46 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 8/30 and the code length 64800.

FIG. 47 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 8/30 and the code length 64800.

FIG. 48 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 9/30 and the code length 64800.

FIG. 49 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 9/30 and the code length 64800.

FIG. 50 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 10/30 and the code length 64800.

FIG. 51 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 10/30 and the code length 64800.

FIG. 52 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 11/30 and the code length 64800.

FIG. 53 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 11/30 and the code length 64800.

FIG. 54 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 12/30 and the code length 64800.

FIG. 55 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 12/30 and the code length 64800.

FIG. 56 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 13/30 and the code length 64800.

FIG. 57 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 13/30 and the code length 64800.

FIG. 58 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 14/30 and the code length 64800.

FIG. 59 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 14/30 and the code length 64800.

FIG. 60 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 15/30 and the code length 64800.

FIG. 61 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 15/30 and the code length 64800.

FIG. 62 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 16/30 and the code length 64800.

FIG. 63 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 16/30 and the code length 64800.

FIG. 64 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 16/30 and the code length 64800.

FIG. 65 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 17/30 and the code length 64800.

FIG. 66 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 17/30 and the code length 64800.

FIG. 67 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 17/30 and the code length 64800.

FIG. 68 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 18/30 and the code length 64800.

FIG. 69 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 18/30 and the code length 64800.

FIG. 70 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 18/30 and the code length 64800.

FIG. 71 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 19/30 and the code length 64800.

FIG. 72 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 19/30 and the code length 64800.

FIG. 73 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 19/30 and the code length 64800.

FIG. 74 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 20/30 and the code length 64800.

FIG. 75 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 20/30 and the code length 64800.

FIG. 76 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 20/30 and the code length 64800.

FIG. 77 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 21/30 and the code length 64800.

FIG. 78 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 21/30 and the code length 64800.

FIG. 79 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 21/30 and the code length 64800.

FIG. 80 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 22/30 and the code length 64800.

FIG. 81 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 22/30 and the code length 64800.

FIG. 82 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 22/30 and the code length 64800.

FIG. 83 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 23/30 and the code length 64800.

FIG. 84 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 23/30 and the code length 64800.

FIG. 85 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 23/30 and the code length 64800.

FIG. 86 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 24/30 and the code length 64800.

FIG. 87 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 24/30 and the code length 64800.

FIG. 88 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 24/30 and the code length 64800.

FIG. 89 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 25/30 and the code length 64800.

FIG. 90 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 25/30 and the code length 64800.

FIG. 91 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 25/30 and the code length 64800.

FIG. 92 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 26/30 and the code length 64800.

FIG. 93 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 26/30 and the code length 64800.

FIG. 94 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 26/30 and the code length 64800.

FIG. 95 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 27/30 and the code length 64800.

FIG. 96 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 27/30 and the code length 64800.

FIG. 97 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 27/30 and the code length 64800.

FIG. 98 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 27/30 and the code length 64800.

FIG. 99 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 28/30 and the code length 64800.

FIG. 100 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 28/30 and the code length 64800.

FIG. 101 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 28/30 and the code length 64800.

FIG. 102 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 28/30 and the code length 64800.

FIG. 103 is a diagram illustrating an example of a parity check matrix initial value table with the code rate 29/30 and the code length 64800.

FIG. 104 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 29/30 and the code length 64800.

FIG. 105 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 29/30 and the code length 64800.

FIG. 106 is a diagram illustrating the example of the parity check matrix initial value table with the code rate 29/30 and the code length 64800.

FIG. 107 is a diagram illustrating an example of a Tanner graph of an ensemble defined by a degree sequence indicating a column weight of 3 and a row weight of 6.

FIG. 108 is a diagram illustrating an example of a Tanner graph of a multi-edge type ensemble.

FIG. 109 is a diagram illustrating minimum cycle lengths and performance thresholds for parity check matrices of LDPC codes with the code length 64800.

FIG. 110 is a diagram depicting a parity check matrix of an LDPC code with the code length 64800.

FIG. 111 is a diagram depicting parity check matrices of LDPC codes with the code length 64800.

FIG. 112 is a diagram illustrating simulated BERs/FERs of LDPC codes with the code length 64800.

FIG. 113 is a diagram illustrating simulated BERs/FERs of LDPC codes with the code length 64800.

FIG. 114 is a diagram illustrating simulated BERs/FERs of LDPC codes with the code length 64800.

FIG. 115 includes diagrams illustrating BCH codes used in simulations of BERs/FERs of LDPC codes with the code length 64800.

FIG. 116 is a block diagram illustrating an example configuration of a receiving device 12.

FIG. 117 is a block diagram illustrating an example configuration of a bit deinterleaver 165.

FIG. 118 is a flowchart depicting a process performed by a QAM decoder 164, the bit deinterleaver 165, and an LDPC decoder 166.

FIG. 119 is a diagram illustrating an example of a parity check matrix of an LDPC code.

FIG. 120 is a diagram illustrating a matrix (transformed parity check matrix) obtained by performing row permutation and column permutation on a parity check matrix.

FIG. 121 is a diagram illustrating a transformed parity check matrix that is divided into 5×5 units.

FIG. 122 is a block diagram illustrating an example configuration of a decoding device that collectively performs node computation for P nodes.

FIG. 123 is a block diagram illustrating an example configuration of the LDPC decoder 166.

FIG. 124 includes diagrams depicting a process of a multiplexer 54 included in the bit deinterleaver 165.

FIG. 125 is a diagram depicting the processing of a column twist deinterleaver 55.

FIG. 126 is a block diagram illustrating another example configuration of the bit deinterleaver 165.

FIG. 127 is a block diagram illustrating a first example configuration of a receiving system in which the receiving device 12 can be used.

FIG. 128 is a block diagram illustrating a second example configuration of the receiving system in which the receiving device 12 can be used.

FIG. 129 is a block diagram illustrating a third example configuration of the receiving system in which the receiving device 12 can be used.

FIG. 130 is a block diagram illustrating an example configuration of an embodiment of a computer to which the present technology applies.

DESCRIPTION OF EMBODIMENTS

[Example Configuration of Transmission System to which Present Technology Applies]

FIG. 7 illustrates an example configuration of an embodiment of a transmission system (the term “system” refers to a logical set of devices or apparatuses, and the devices or apparatuses may or may not be accommodated in the same housing) to which the present technology applies.

Referring to FIG. 7, the transmission system includes a transmitting device 11 and a receiving device 12.

The transmitting device 11 is configured to transmit (or broadcast) data such as a television broadcast program. More specifically, the transmitting device 11 encodes the target data to be transmitted, such as image data and audio data of a program, into an LDPC code, and transmits the LDPC code via a communication path 13 such as a satellite link, a terrestrial link, or a cable (wired line).

The receiving device 12 receives an LDPC code transmitted from the transmitting device 11 via the communication path 13, decodes the LDPC code into target data, and outputs the target data.

Here, it is well established that an LDPC code used in the transmission system illustrated in FIG. 7 exhibits very high performance on an AWGN (Additive White Gaussian Noise) communication path.

However, burst errors or erasures may occur in the communication path 13. For example, notably in a case where the communication path 13 is a terrestrial link, in an OFDM (Orthogonal Frequency Division Multiplexing) system, a specific symbol may drop to zero in power (or be erased) in accordance with the delay of an echo (which is a path other than the main path) in a multi-path environment where a D/U (Desired to Undesired Ratio) is 0 dB (i.e., the power of the echo as the undesired power is equal to the power of the main path as the desired power).

Further, if the D/U is 0 dB, all OFDM symbols at a specific point in time may also drop to zero in power (or erased) due to a Doppler (dopper) frequency in a flutter (which is a communication path to which an echo with a Doppler frequency applied and having a delay of 0 is added).

In addition, burst errors may occur due to unstable power of the receiving device 12 or undesired wiring conditions from a receiver (not illustrated) that receives a signal from the transmitting device 11, such as an antenna, on the receiving device 12 side to the receiving device 12.

In the LDPC code decoding process, on the other hand, as described above with reference to FIG. 5, the variable node computation of Expression (1), which involves addition of (the reception values u_(0i) of) the code bits of the LDPC code, is performed at the respective columns of the parity check matrix H, that is, the variable nodes corresponding to the code bits of the LDPC code. Thus, an error occurring in a code bit used for variable node computation would reduce the accuracy of a determined message.

In the LDPC code decoding process, furthermore, the check node computation of Expression (7) is performed at a check node, by using messages determined at the variable nodes connected to the check node. Thus, an increase in the number of check nodes for which errors (including erasures) simultaneously occur in (code bits of an LDPC code corresponding to) a plurality of connected variable nodes would reduce decoding performance.

More specifically, for example, if two or more of variable nodes connected to a check node simultaneously become erasures, the check node returns a message with the probability of the value 0 being equal to the probability of the value 1 to all the variable nodes. In this case, the check node that returns the message with equal probabilities does not contribute to single decoding processing (one set of variable node computation and check node computation), resulting in a larger number of repetitions of decoding processing. Thus, decoding performance may deteriorate, and, additionally, the power consumption of the receiving device 12 that decodes the LDPC code may increase.

To address the inconveniences described above, the transmission system illustrated in FIG. 7 is capable of increasing the resistance to burst errors or erasures while maintaining performance in an AWGN communication path.

[Example Configuration of Transmitting Device 11]

FIG. 8 is a block diagram illustrating an example configuration of the transmitting device 11 illustrated in FIG. 7.

In the transmitting device 11, one or more input streams as target data are supplied to a mode adaptation/multiplexer 111.

The mode adaptation/multiplexer 111 performs processing such as mode selection and multiplexing the supplied one or more input streams, if necessary, and supplies the resulting data to a padder 112.

The padder 112 pads zeros (or adds null) to the data supplied from the mode adaptation/multiplexer 111, as necessary, and supplies the resulting data to a BB scrambler 113.

The BB scrambler 113 applies BB scrambling (Base-Band Scrambling) to the data supplied from the padder 112, and supplies the resulting data to a BCH encoder 114.

The BCH encoder 114 performs BCH encoding on the data supplied from the BB scrambler 113, and supplies the resulting data to an LDPC encoder 115 as LDPC target data to be subjected to LDPC encoding.

The LDPC encoder 115 performs LDPC encoding on the LDPC target data supplied from the BCH encoder 114 in accordance with a parity check matrix of an LDPC code, in which a parity matrix that is a portion of parity bits of the LDPC code has a stepwise structure, to obtain an LDPC code having information bits corresponding to the LDPC target data. The LDPC encoder 115 outputs the LDPC code.

More specifically, the LDPC encoder 115 performs LDPC encoding to encode the LDPC target data into, for example, an LDPC code defined in a certain standard such as DVB-S.2, DVB-T.2, or DVB-C.2 (corresponding to a parity check matrix) or a predetermined LDPC code (corresponding to a parity check matrix), and outputs the resulting LDPC code.

Here, an LDPC code defined in the DVB-S.2, DVB-T.2, or DVB-C.2 standard is an IRA (Irregular Repeat Accumulate) code, and a parity matrix in a parity check matrix of the LDPC code has a stepwise structure. The parity matrix and the stepwise structure will be described below. An example of the IRA code is described in, for example, “Irregular Repeat-Accumulate Codes,” H. Jin, A. Khandekar, and R. J. McEliece, in Proceedings of 2nd International Symposium on Turbo Codes and Related Topics, pp. 1-8, September 2000.

The LDPC code output from the LDPC encoder 115 is supplied to a bit interleaver 116.

The bit interleaver 116 performs bit interleaving, described below, on the LDPC code supplied from the LDPC encoder 115, and supplies the LDPC code that has been subjected to bit interleaving to a QAM encoder 117.

The QAM encoder 117 maps the LDPC code supplied from the bit interleaver 116 to constellation points each representing one symbol of orthogonal modulation in units of one or more code bits of the LDPC code (or in units of symbols), and performs orthogonal modulation (multi-level modulation).

More specifically, the QAM encoder 117 maps the LDPC code supplied from the bit interleaver 116 to constellation points defined by the modulation scheme on which orthogonal modulation of the LDPC code is based, in an IQ plane (IQ constellation) defined by an I axis representing an I component that is in the same phase as that of the carrier and a Q axis representing a Q component orthogonal to the carrier, and performs orthogonal modulation.

Here, examples of the modulation scheme on which the orthogonal modulation performed by the QAM encoder 117 is based include modulation schemes defined in the DVB-S.2, DVB-T.2, DVB-C.2, and similar standards, and other modulation schemes, examples of which include BPSK (Binary Phase Shift Keying), QPSK (Quadrature Phase Shift Keying), 16APSK (Amplitude Phase-Shift Keying), 32APSK, 16QAM (Quadrature Amplitude Modulation), 64QAM, 256QAM, 1024QAM, 4096QAM, and 4PAM (Pulse Amplitude Modulation). Which of the modulation schemes the QAM encoder 117 uses to perform orthogonal modulation is set in advance through, for example, operation or the like by an operator of the transmitting device 11.

The data obtained by the processing of the QAM encoder 117 (i.e., the symbols mapped to the constellation points) is supplied to a time interleaver 118.

The time interleaver 118 performs time interleaving (which is interleaving in the time domain) on the data (i.e., symbols) supplied from the QAM encoder 117 in units of symbols, and supplies the resulting data to a MISO/MIMO encoder 119.

The MISO/MIMO encoder 119 performs space-time encoding on the data (i.e., symbols) supplied from the time interleaver 118, and supplies the resulting data to a frequency interleaver 120.

The frequency interleaver 120 performs frequency interleaving (which is interleaving in the frequency domain) on the data (i.e., symbols) supplied from the MISO/MIMO encoder 119 in units of symbols, and supplies the resulting data to a frame builder & resource allocation unit 131.

On the other hand, control data (signalling) for transmission control, such as BB signalling (Base Band Signalling) (BB Header), is supplied to a BCH encoder 121.

The BCH encoder 121 performs BCH encoding on the control data supplied thereto in a manner similar to that for the BCH encoder 114, and supplies the resulting data to an LDPC encoder 122.

The LDPC encoder 122 performs LDPC encoding on the data supplied from the BCH encoder 121, as LDPC target data, in a manner similar to that for the LDPC encoder 115, and supplies the resulting LDPC code to a QAM encoder 123.

The QAM encoder 123 maps the LDPC code supplied from the LDPC encoder 122 to constellation points each representing one symbol of orthogonal modulation, in units of one or more code bits of the LDPC code (i.e., in units of symbols) in a manner similar to that for the QAM encoder 117, and performs orthogonal modulation. The QAM encoder 123 supplies the resulting data (i.e., symbols) to a frequency interleaver 124.

The frequency interleaver 124 performs frequency interleaving on the data (i.e., symbols) supplied from the QAM encoder 123 in units of symbols in a manner similar to that for the frequency interleaver 120, and supplies the resulting data to the frame builder & resource allocation unit 131.

The frame builder & resource allocation unit 131 adds pilot symbols at desired positions of the data (i.e., symbols) supplied from the frequency interleavers 120 and 124, and configures a frame including a certain number of symbols (for example, a PL (Physical Layer) frame, a T2 frame, a C2 frame, etc.) from the resulting data (i.e., symbols). The frame builder & resource allocation unit 131 supplies the frame to an OFDM generation unit 132.

The OFDM generation unit 132 generates an OFDM signal from the frame supplied from the frame builder & resource allocation unit 131, corresponding to the frame, and transmits the OFDM signal via the communication path 13 (FIG. 7).

Note that the transmitting device 11 may be configured without including some of the blocks illustrated in FIG. 8, such as the time interleaver 118, the MISO/MIMO encoder 119, the frequency interleaver 120, and the frequency interleaver 124.

FIG. 9 illustrates an example configuration of the bit interleaver 116 illustrated in FIG. 8.

The bit interleaver 116 is a data processing device for interleaving data, and includes a parity interleaver 23, a column twist interleaver 24, and a demultiplexer (DEMUX) 25. Note that the bit interleaver 116 may be configured without including one or both of the parity interleaver 23 and the column twist interleaver 24.

The parity interleaver 23 performs parity interleaving on the LDPC code supplied from the LDPC encoder 115 to interleave parity bits of the LDPC code to different parity bit positions, and supplies the LDPC code that has been subjected to parity interleaving to the column twist interleaver 24.

The column twist interleaver 24 performs column twist interleaving on the LDPC code supplied from the parity interleaver 23, and supplies the LDPC code that has been subjected to column twist interleaving to the demultiplexer 25.

More specifically, the LDPC code is transmitted after one or more code bits of the LDPC code are mapped to a constellation point representing one symbol of orthogonal modulation using the QAM encoder 117 illustrated in FIG. 8.

The column twist interleaver 24 performs reordering processing, for example, column twist interleaving, described below, to reorder the code bits of the LDPC code supplied from the parity interleaver 23 so that a plurality of code bits of the LDPC code corresponding to is in an arbitrary row of the parity check matrix used in the LDPC encoder 115 are not included in one symbol.

The demultiplexer 25 performs permutation processing on the LDPC code supplied from the column twist interleaver 24 to permute the positions of two or more code bits of the LDPC code to be mapped to symbols, thereby obtaining an LDPC code with increased resistance to AWGN. The demultiplexer 25 then supplies the two or more code bits of the LDPC code, which are obtained through the permutation processing, to the QAM encoder 117 (FIG. 8) as a symbol.

Next, FIG. 10 illustrates the parity check matrix H that the LDPC encoder 115 illustrated in FIG. 8 uses for LDPC encoding.

The parity check matrix H has an LDGM (Low-Density Generation Matrix) structure, and can be expressed by the equation H=[H_(A)|H_(T)] (which is a matrix whose left elements are the elements of an information matrix H_(A) and right elements are the elements of a parity matrix H_(T)), where the information matrix H_(A) is a portion corresponding to information bits and the parity matrix H_(T) is a portion corresponding to parity bits among the code bits of the LDPC code.

Here, the number of information bits and the number of parity bits among the code bits of one LDPC code (i.e., one code word) are represented by an information length K and a parity length M, respectively. In addition, the number of code bits of one LDPC code is represented by a code length N (=K+M).

The information length K and the parity length M of an LDPC code having a certain code length N are determined in accordance with the code rate. In addition, the parity check matrix H is a matrix having M rows and N columns. Thus, the information matrix H_(A) is an M×K matrix, and the parity matrix H_(T) is an M×M matrix.

FIG. 11 illustrates a parity matrix H_(T) of a parity check matrix H of an LDPC code defined in the DVB-S.2, DVB-T.2, and DVB-C.2 standards.

As illustrated in FIG. 11, the parity matrix H_(T) of the parity check matrix H of the LDPC code defined in DVB-T.2 and similar standards is a matrix having a stepwise structure (i.e., a lower bidiagonal matrix) in which elements of 1 are arranged in a stepwise manner. The parity matrix H_(T) has a row weight of 1 for the first row and a row weight of 2 for all the remaining rows. The parity matrix H_(T) further has a column weight of 1 for the last column and a column weight of 2 for all the remaining columns.

In the manner described above, an LDPC code of a parity check matrix H including a parity matrix H_(T) having a stepwise structure can be easily generated using the parity check matrix H.

More specifically, an LDPC code (i.e., a code word) is represented by a row vector c, and a column vector obtained by transposing the row vector is represented by c^(T). In the row vector c, which is the LDPC code, furthermore, an information bit portion is represented by a row vector A, and a parity bit portion is represented by a row vector T.

In this case, the row vector c can be expressed by the equation c=[A|T] (which is a row vector whose left elements are the elements of a row vector A and right elements are the elements of a row vector T), where the row vector A corresponds to information bits and the row vector T corresponds to parity bits.

It is necessary for the parity check matrix H and the row vector c=[A|T], which serves as the LDPC code, to satisfy the equation Hc^(T)=0. Thus, the values of the elements of the row vector T corresponding to parity bits in the row vector c=[A|T] satisfying the equation Hc^(T)=0 can be sequentially (or successively) determined by setting the elements in the respective rows of the column vector Hc^(T) in the equation Hc^(T)=0 to zero in order, starting from the element in the first row, in a case where the parity matrix H_(T) in the parity check matrix H=[H_(A)|H_(T)] has the stepwise structure illustrated in FIG. 11.

FIG. 12 is a diagram depicting a parity check matrix H of an LDPC code defined in DVB-T.2 and similar standards.

The parity check matrix H of the LDPC code defined in DVB-T.2 and similar standards has a column weight X for KX columns, starting with the first column, a column weight of 3 for the subsequent K3 columns, a column weight of 2 for the subsequent (M−1) columns, and a column weight of 1 for the last column.

Here, the sum of columns given by KX+K3+M−1+1 equals the code length N.

FIG. 13 is a diagram illustrating the numbers of columns KX, K3, and M and the column weight X for the respective code rates r of LDPC codes defined in DVB-T.2 and similar standards.

In DVB-T.2 and similar standards, LDPC codes having code lengths N of 64800 bits and 16200 bits are defined.

In addition, 11 code rates (nominal rates), 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 8/9, and 9/10, are defined for an LDPC code with a code length N of 64800 bits, and 10 code rates, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, and 8/9, are defined for an LDPC code with a code length N of 16200 bits.

Hereinafter, the code length N of 64800 bits will also be referred to as “64k bits”, and the code length N of 16200 bits will also be referred to as “16k bits”.

It is well established that a code bit of an LDPC code corresponding to a column with a higher column weight in a parity check matrix H has a lower error rate.

In a parity check matrix H defined in DVB-T.2 and similar standards illustrated in FIGS. 12 and 13, the column weight tends to increase as the ordinal number of the columns of the parity check matrix H decreases (i.e., as the column comes closer to the left end of the parity check matrix H). Accordingly, robustness to errors (or resistance to errors) tends to increase as the ordinal number of the code bits of an LDPC code corresponding to the parity check matrix H decreases (i.e., the first code bit tends to be the most robust to errors), and tends to decrease as the ordinal number of the code bits increases (i.e., the last code bit tends to be the least robust to errors).

Next, FIG. 14 illustrates example arrangements of (constellation points corresponding to) 16 symbols in an IQ plane in a case where the QAM encoder 117 illustrated in FIG. 8 performs 16QAM operation.

More specifically, part A of FIG. 14 illustrates symbols of DVB-T.2 16QAM.

In 16QAM, one symbol is represented as 4 bits, and 16 (=2⁴) symbols are provided. Further, the 16 symbols are arranged in a square of 4 symbols in the I direction and 4 symbols in the Q direction, centered on the origin of the IQ plane.

Assuming now that the (i+1)-th bit from the most significant bit of a bit sequence represented by one symbol is represented by bit y_(i), then 4 bits represented by one symbol of 16QAM can be represented by bits y₀, y₁, y₂, and y₃ in order, starting from the most significant bit. In a case where the modulation scheme is 16QAM, 4 code bits of an LDPC code are (symbolized) to a symbol (symbol values) of 4 bits y₀ to y₃.

Part B of FIG. 14 illustrates bit boundaries of 4 bits (hereinafter also referred to as “symbol bits”) y₀ to y₃ represented by a 16QAM symbol.

Here, a bit boundary of symbol bits y_(i) (in FIG. 14, i=0, 1, 2, 3) is a boundary between a symbol having a symbol bit y_(i) of 0 and a symbol having a symbol bit y_(i) of 1.

As illustrated in part B of FIG. 14, for the most significant symbol bit y₀ among the 4 symbol bits y₀ to y₃ represented by the 16QAM symbol, the only one bit boundary extends along the Q axis in the IQ plane. For the second symbol bit y₁ (the second most significant bit), the only one bit boundary extends along the I axis in the IQ plane.

In addition, two bit boundaries are provided for the third symbol bit y₂, one between the first and second columns of the 4×4 square of symbols, counting from the left, and the other between the third and fourth columns.

In addition, two bit boundaries are provided for the fourth symbol bit y₃, one between the first and second rows of the 4×4 square of symbols, counting from the top, and the other between the third and fourth rows.

Symbol bits y_(i) represented by symbols are less erroneous (i.e., lower error probability) as the number of symbols spaced away from a bit boundary increases, and are more erroneous (i.e., higher error probability) as the number of symbols close to a bit boundary increases.

It is assumed now that a less erroneous bit (robust to errors) is referred to as a “strong bit” and a more erroneous bit (sensitive to errors) is referred to as a “weak bit”. In the 4 symbol bits y₀ to y₃ of the 16QAM symbol, the most significant symbol bit y₀ and the second symbol bit y₁ are strong bits, and the third symbol bit y₂ and the fourth symbol bit y₃ are weak bits.

FIGS. 15 to 17 illustrate example arrangements of (constellation points corresponding to) 64 symbols in an IQ plane in a case where the QAM encoder 117 illustrated in FIG. 8 performs 64QAM operation, that is, symbols of DVB-T.2 16QAM.

In 64QAM, one symbol represents 6 bits, and 64 (=2⁶) symbols are provided. Further, the 64 symbols are arranged in a square of 8 symbols in the I direction and 8 symbols in the Q direction, centered on the origin of the IQ plane.

Symbol bits of one 64QAM symbol can be represented by bits y₀, y₁, y₂, y₃, y₄, and y₅ in order, starting from the most significant bit. In a case where the modulation scheme is 64QAM, 6 code bits of an LDPC code are mapped to a symbol of 6-bit symbol bits y₀ to y₅.

Here, FIG. 15 illustrates bit boundaries of the most significant symbol bit y₀ and the second symbol bit y₁ among the symbol bits y₀ to y₅ of the 64QAM symbol, FIG. 16 illustrates bit boundaries of the third symbol bit y₂ and the fourth symbol bit y₃, and FIG. 17 illustrates bit boundaries of the fifth symbol bit y₄ and the sixth symbol bit y₅.

As illustrated in FIG. 15, one bit boundary is provided for each of the most significant symbol bit y₀ and the second symbol bit y₁. Further, as illustrated in FIG. 16, two bit boundaries are provided for each of the third symbol bit y₂ and the fourth symbol bit y₃. As illustrated in FIG. 17, four bit boundaries are provided for each of the fifth symbol bit y₄ and the sixth symbol bit y₅.

Accordingly, among the symbol bits y₀ to y₅ of the 64QAM symbol, the most significant symbol bit y₀ and the second symbol bit y₁ are the strongest bits, and the third symbol bit y₂ and the fourth symbol bit y₃ are the second strongest bits. Then, the fifth symbol bit y₄ and the sixth symbol bit y₅ are weak bits.

It can be found from FIG. 14 and, furthermore, FIGS. 15 to 17 that symbol bits of an orthogonal modulation symbol have a tendency that more significant bits are stronger bits and less significant bits are weaker bits.

FIG. 18 is a diagram illustrating an example arrangement of (constellation points corresponding to) 4 symbols in an IQ plane in a case where a satellite link is used as the communication path 13 (FIG. 7) and the QAM encoder 117 illustrated in FIG. 8 performs QPSK operation, that is, a diagram of, for example, DVB-S.2 QPSK symbols.

In DVB-S.2 QPSK, each symbol is mapped to one of four constellation points on the circumference of a circle having a radius ρ of 1, centered on the origin of the IQ plane.

FIG. 19 is a diagram illustrating an example arrangement of 8 symbols in an IQ plane in a case where a satellite link is used as the communication path 13 (FIG. 7) and the QAM encoder 117 illustrated in FIG. 8 performs 8PSK operation, that is, a diagram of, for example, DVB-S.2 8PSK symbols.

In DVB-S.2 8PSK, each symbol is mapped to one of eight constellation points on the circumference of a circle having a radius ρ of 1, centered on the origin of the IQ plane.

FIG. 20 includes diagrams illustrating an example arrangement of 16 symbols in an IQ plane in a case where a satellite link is used as the communication path 13 (FIG. 7) and the QAM encoder 117 illustrated in FIG. 8 performs 16APSK operation, that is, diagrams of, for example, DVB-S.2 16APSK symbols.

Part A of FIG. 20 illustrates an arrangement of constellation points of DVB-S.2 16APSK.

In DVB-S.2 16APSK, each symbol is mapped to one of 16 constellation points in total, namely, 4 constellation points on the circumference of a circle having a radius R₁ and 12 constellation points on the circumference of a circle having a radius R₂ (>R₁), centered on the origin of the IQ plane.

Part B of FIG. 20 illustrates the ratio γ=R₂/R₁, which is the ratio of the radii R₂ and R₁ in the arrangement of constellation points of DVB-S.2 16APSK.

In the arrangement of constellation points of DVB-S.2 16APSK, the ratio γ of the radii R₂ and R₁ differs depending on the code rate.

FIG. 21 includes diagrams illustrating an example arrangement of 32 symbols in an IQ plane in a case where a satellite link is used as the communication path 13 (FIG. 7) and the QAM encoder 117 illustrated in FIG. 8 performs 32APSK operation, that is, diagrams of, for example, DVB-S.2 32APSK symbols.

Part A of FIG. 21 illustrates an arrangement of constellation points of DVB-S.2 32APSK.

In DVB-S.2 32APSK, each symbol is mapped to one of 32 constellation points in total, namely, 4 constellation points on the circumference of a circle having a radius R₁, 12 constellation points on the circumference of a circle having a radius R₂ (>R₁), and 16 constellation points on the circumference of a circle having a radius R₃ (>R₂), centered on the origin of the IQ plane.

Part B of FIG. 21 illustrates the ratio γ₁=R₂/R₁, which is the ratio of the radii R₂ and R₁, and the ratio γ₂=R₃/R₁, which is the ratio of the radii R₃ and R₁, in the arrangement of constellation points of DVB-S.2 32APSK.

In the arrangement of constellation points of DVB-S.2 32APSK, the ratio γ₁ of the radii R₂ and R₁ and the ratio γ₂ of the radii R₃ and R₁ each differ depending on the code rate.

The symbol bits of the symbols of the respective DVB-S.2 orthogonal modulation types (QPSK, 8PSK, 16APSK, and 32APSK) having the arrangements of constellation points illustrated in FIGS. 18 to 21 also include strong bits and weak bits similarly to those illustrated in FIGS. 14 to 17.

Here, as described above with reference to FIGS. 12 and 13, the LDPC code output from the LDPC encoder 115 (FIG. 8) includes code bits robust to errors and code bits sensitive to errors.

Furthermore, as described above with reference to FIGS. 14 to 21, the symbol bits of a symbol of orthogonal modulation performed by the QAM encoder 117 include strong bits and weak bits.

Thus, assigning code bits of an LDPC code which are sensitive to errors to symbol bits of an orthogonal modulation symbol which are sensitive to errors would reduce the resistance to errors as a whole.

Accordingly, an interleaver has been proposed that is configured to interleave code bits of an LDPC code such that a code bit of the LDPC code which is sensitive to errors is allocated to a strong bit (symbol bit) of an orthogonal modulation symbol.

The demultiplexer 25 illustrated in FIG. 9 is capable of performing the processing of the above-described interleaver.

FIG. 22 includes diagrams depicting the processing of the demultiplexer 25 illustrated in FIG. 9.

More specifically, part A of FIG. 22 illustrates an example functional configuration of the demultiplexer 25.

The demultiplexer 25 includes a memory 31 and a permutation unit 32.

An LDPC code is supplied to the memory 31 from the LDPC encoder 115.

The memory 31 has a storage capacity to store mb bits in its row (horizontal) direction and N/(mb) bits in its column (vertical) direction. Code bits of the LDPC code supplied to the memory 31 are written in the column direction, and are read in the row direction. The read code bits are supplied to the permutation unit 32.

Here, as described above, N(=information length K+parity length M) represents the code length of the LDPC code.

In addition, m represents the number of code bits of the LDPC code which are mapped to one symbol, and b is a certain positive integer and denotes a multiple used to obtain integer multiples of m. As described above, the demultiplexer 25 maps (or symbolizes) code bits of an LDPC code to a symbol, where the multiple b represents the number of symbols obtained by the demultiplexer 25 through single symbolization.

Part A of FIG. 22 illustrates an example configuration of the demultiplexer 25 in a case where the modulation scheme is 64QAM in which each symbol is mapped to one of 64 constellation points, or any other suitable modulation scheme. The number of code bits m of an LDPC code to be mapped to one symbol is therefore 6.

In part A of FIG. 22, furthermore, the multiple b is 1. Therefore, the memory 31 has a storage capacity of N/(6×1) bits in the column direction and (6×1) bits in the row direction.

Here, in the following, a storage area of the memory 31, which has one bit in the row direction and extends in the column direction, is referred to as a “column” as appropriate. In part A of FIG. 22, the memory 31 includes 6 (=6×1) columns.

The demultiplexer 25 writes code bits of the LDPC code to the memory 31 (in the column direction) from the top to the bottom of each column of the memory 31, where the writing operation moves toward the right, starting from the leftmost column.

Further, when the writing of code bits up to the bottom of the rightmost column is completed, code bits are read from the memory 31 in the row direction, starting from the first row of all the columns of the memory 31, in units of 6 bits (i.e., mb bits). The read code bits are supplied to the permutation unit 32.

The permutation unit 32 performs permutation processing to permute the positions of 6 code bits supplied from the memory 31, and outputs the resulting 6 bits as 6 symbol bits y₀, y₁, y₂, y₃, y₄, and y₅ representing one 64QAM symbol.

More specifically, mb (here, 6) code bits are read from the memory 31 in the row direction. If the i-th bit from the most significant bit of the mb code bits read from the memory 31 is represented by bit b_(i) (where i=0, 1, . . . , mb−1), the 6 code bits read from the memory 31 in the row direction can be represented by bits b₀, b₁, b₂, b₃, b₄, and b₅ in order, starting from the most significant bit.

In terms of the column weights described with reference to FIGS. 12 and 13, the code bits in the bit b₀ direction are code bits robust to errors, and the code bits in the bit b₅ direction are code bits sensitive to errors.

The permutation unit 32 is configured to perform permutation processing to permute the positions of the 6 code bit b₀ to b₅ read from the memory 31 so that the code bits sensitive to errors among the 6 code bits b₀ to b₅ read from the memory 31 may be allocated to strong bits among the symbol bits y₀ to y₅ representing one 64QAM symbol.

Here, various methods for permuting the 6 code bits b₀ to b₅ read from the memory 31 and allocating them to the 6 symbol bits y₀ to y₅ representing one 64QAM symbol have been proposed by many companies.

Part B of FIG. 22 illustrates a first permutation method, part C of FIG. 22 illustrates a second permutation method, and part D of FIG. 22 illustrates a third permutation method.

In part B of FIG. 22 to part D of FIG. 22 (also in FIG. 23, described below), a line connecting bits b_(i) and y_(j) indicates that the code bit b_(i) is allocated to the symbol bit y_(j) of the symbol (i.e., the position of the code bit b_(i) is replaced with that of the symbol bit y_(j)).

In the first permutation method illustrated in part B of FIG. 22, the use of one of three permutation types is proposed. In the second permutation method illustrated in part C of FIG. 22, the use of one of two permutation types is proposed.

In the third permutation method illustrated in part D of FIG. 22, the sequential selection and use of six permutation types are proposed.

FIG. 23 illustrates an example configuration of the demultiplexer 25 in a case where the modulation scheme is 64QAM in which each symbol is mapped to one of 64 constellation points, or any other suitable modulation scheme (and therefore, the number of code bits m of an LDPC code to be mapped to one symbol is 6, similarly to the case in FIG. 22) and in a case where the multiple b is 2, and also illustrates a fourth permutation method.

In a case where the multiple b is 2, the memory 31 has a storage capacity of N/(6×2) bits in the column direction and (6×2) bits in the row direction, and includes 12 (=6×2) columns.

Part A of FIG. 23 illustrates the order in which code bits of an LDPC code are written to the memory 31.

As described with reference to FIG. 22, the demultiplexer 25 writes code bits of the LDPC code to the memory 31 (in the column direction) from the top to the bottom of each column of the memory 31, where the writing operation moves toward the right, starting from the leftmost column.

Further, when the writing of code bits up to the bottom of the rightmost column is completed, code bits are read from the memory 31 in the row direction, starting from the first row of all the columns of the memory 31, in units of 12 bits (i.e., mb bits). The read code bits are supplied to the permutation unit 32.

The permutation unit 32 performs permutation processing to permute the positions of 12 code bits supplied from the memory 31, by using the fourth permutation method, and outputs the resulting 12 bits as 12 bits representing two symbols of 64QAM (i.e., b symbols), that is, 6 symbol bits y₀, y₁, y₂, y₃, y₄, and y₅ representing one 64QAM symbol and 6 symbol bits y₀, y₁, y₂, y₃, y₄, and y₅ representing the subsequent one symbol.

Here, part B of FIG. 23 illustrates a fourth permutation method that is a method for performing permutation processing by the permutation unit 32 illustrated in part A of FIG. 23.

Note that, in the permutation processing, in a case where the multiple b is 2 (also in a case where the multiple b is 3 or more), mb code bits are allocated to mb symbol bits of consecutive b symbols. In the following, including FIG. 23, the (i+1)-th bit from the most significant bit of mb symbol bits of consecutive b symbols is represented by bit (or symbol bit) y₁, for convenience of illustration.

The optimum permutation type of code bits, which increases the error-rate performance in an AWGN communication path, depends on the code rate or code length of an LDPC code, the modulation scheme, and so forth.

[Parity Interleaving]

Next, parity interleaving performed by the parity interleaver 23 illustrated in FIG. 9 will be described with reference to FIGS. 24 to 26.

FIG. 24 illustrates (part of) a Tanner graph of a parity check matrix of an LDPC code.

As illustrated in FIG. 24, if errors such as erasures simultaneously occur in multiple, such as two, (code bits corresponding to) variable nodes connected to a check node, the check node returns a message with the probability of the value 0 being equal to the probability of the value 1 to all the variable nodes connected to the check node. Hence, the decoding performance deteriorates if a plurality of variable nodes connected to the same check node simultaneously become erasures or the like.

Meanwhile, the LDPC code output from the LDPC encoder 115 illustrated in FIG. 8, which is defined in the DVB-S.2 and similar standards, is an IRA code, and a parity matrix H_(T) of the parity check matrix H has a stepwise structure, as illustrated in FIG. 11.

FIG. 25 illustrates a parity matrix H_(T) having a stepwise structure, and a Tanner graph corresponding to the parity matrix H_(T).

More specifically, part A of FIG. 25 illustrates a parity matrix H_(T) having a stepwise structure, and part B of FIG. 25 illustrates a Tanner graph corresponding to the parity matrix H_(T) illustrated in part A of FIG. 25.

In the parity matrix H_(T) having a stepwise structure, elements of 1 are adjacent in each row (except the first row). Thus, in the Tanner graph of the parity matrix H_(T), two adjacent variable nodes corresponding to two adjacent elements having the value 1 in the parity matrix H_(T) are connected to the same check node.

Accordingly, if errors simultaneously occur in parity bits corresponding two adjacent variable nodes as described above due to burst errors, erasures, and the like, a check node connected to the two variable nodes (i.e., variable nodes whose messages are determined using the parity bits) corresponding to the two erroneous parity bits returns a message with the probability of the value 0 being equal to the probability of the value 1 to the variable nodes connected to the check node. The decoding performance thus deteriorates. Then, if the burst length (which is the number of consecutive erroneous parity bits) increases, the number of check nodes that return the message with equal probabilities increases, resulting in further deterioration of decoding performance.

Accordingly, the parity interleaver 23 (FIG. 9) performs parity interleaving on the LDPC code supplied from the LDPC encoder 115 to interleave parity bits to different parity bit positions in order to prevent the deterioration of decoding performance described above.

FIG. 26 illustrates a parity matrix H_(T) of a parity check matrix H corresponding to an LDPC code which has been subjected to parity interleaving by the parity interleaver 23 illustrated in FIG. 9.

Here, the information matrix H_(A) of the parity check matrix H corresponding to the LDPC code defined in the DVB-S.2 and similar standards, which is output from the LDPC encoder 115, has a cyclic structure.

The term “cyclic structure” refers to a structure in which a certain column matches another column that is cyclically shifted. Examples of the cyclic structure include a structure in which the position of “1” in each row of every P columns corresponds to the position to which the position of the first column out of the P columns has been cyclically shifted in a column direction by a value proportional to the value q obtained by dividing the parity length M. In the following, the number of columns P in the cyclic structure will be referred to as the “number of unit columns of the cyclic structure” as appropriate.

As described with reference to FIGS. 12 and 13, examples of the LDPC codes defined in the DVB-S.2 and similar standards include two types of LDPC codes having code lengths N of 64800 bits and 16200 bits. For either of the two types of LDPC codes, the number of unit columns P of the cyclic structure is defined to be 360, which is one of the divisors, excluding 1 and M, of the parity length M.

In addition, the parity length M has a value other than the prime number represented by the equation M=q×P=q×360, by using a value q which differs depending on the code rate. Therefore, similarly to the number of unit columns P of the cyclic structure, the value q is also one of the divisors, excluding 1 and M, of the parity length M, and is given by dividing the parity length M by the number of unit columns P of the cyclic structure (i.e., the parity length M is the product of the divisors P and q of the parity length M).

As described above, the parity interleaver 23 performs parity interleaving on an N-bit LDPC code to interleave the (K+qx+y+1)-th code bit among the code bits of the N-bit LDPC code to the (K+Py+x+1)-th code bit position, where K denotes the information length, x is an integer greater than or equal to 0 and less than P, and y is an integer greater than or equal to 0 and less than q.

The (K+qx+y+1)-th code bit and the (K+Py+x+1)-th code bit are code bits positioned after the (K+1)-th code bit, and are therefore parity bits. Accordingly, the position of a parity bit of an LDPC code is shifted by parity interleaving.

In this parity interleaving operation, (parity bits corresponding to) variable nodes connected to the check node are spaced away from each other by the number of unit columns P of the cyclic structure, i.e., in the illustrated example, 360 bits, thereby preventing simultaneous occurrence of errors in a plurality of variable nodes connected to the same check node for a burst length less than 360 bits. The resistance to burst errors can therefore be improved.

Note that the LDPC code, which has undergone parity interleaving such that the (K+qx+y+1)-th code bit is interleaved to the (K+Py+x+1)-th code bit position, is identical to an LDPC code of a parity check matrix (hereinafter also referred to as a “transformed parity check matrix”) that is obtained through column permutation to replace the (K+qx+y+1)-th column of the original parity check matrix H with the (K+Py+x+1)-th column.

Furthermore, as illustrated in FIG. 26, the parity matrix of the transformed parity check matrix has a pseudo-cyclic structure whose number of unit columns is P (in FIG. 26, 360).

The term “pseudo-cyclic structure”, as used herein, refers to a structure in which a portion of a matrix has a cyclic structure. A transformed parity check matrix produced by performing column permutation, corresponding to parity interleaving, on a parity check matrix of an LDPC code defined in the DVB-S.2 and similar standards has a portion of 360 rows and 360 columns in a right corner portion thereof (which corresponds to a shift matrix described below) in which only one element of “1” is missing (i.e., an element of “0” appears). In this regard, this cyclic structure is not a complete cyclic structure, called a pseudo-cyclic structure.

Note that the transformed parity check matrix illustrated in FIG. 26 is a matrix obtained by performing permutation of rows (row permutation), in addition to column permutation corresponding to parity interleaving, on the original parity check matrix H such that the transformed parity check matrix includes component matrices described below.

[Column Twist Interleaving]

Next, column twist interleaving as reordering processing performed by the column twist interleaver 24 illustrated in FIG. 9 will be described with reference to FIGS. 27 to 30.

The transmitting device 11 illustrated in FIG. 8 transmits one or more code bits of an LDPC code as one symbol. More specifically, for example, QPSK is used as a modulation scheme for the transmission of 2 code bits as one symbol, and 16APSK or 16QAM is used as a modulation scheme for the transmission of 4 code bits as one symbol.

In a case where 2 code bits are to be transmitted as one symbol, an error such as an erasure occurring in a certain symbol may cause all the code bits of the symbol to be erroneous (or erasures).

Accordingly, in order to reduce the probability of a plurality of (code bits corresponding to) variable nodes connected to the same check node becoming simultaneously erasures to improve decoding performance, it is necessary to prevent variable nodes corresponding to code bits of one symbol from being connected to the same check node.

In contrast, in the parity check matrix H of the LDPC code defined in the DVB-S.2 and similar standards, which is output from the LDPC encoder 115, as described above, the information matrix H_(A) has a cyclic structure and the parity matrix H_(T) has a stepwise structure. In addition, as described with reference to FIG. 26, in a transformed parity check matrix, which is a parity check matrix of an LDPC code that has been subjected to parity interleaving, the parity matrix also has a cyclic structure (more specifically, as described above, a pseudo-cyclic structure).

FIG. 27 illustrates a transformed parity check matrix.

More specifically, part A of FIG. 27 illustrates a transformed parity check matrix of a parity check matrix H of an LDPC code having a code length N of 64800 bits and a code rate (r) of 3/4.

In the transformed parity check matrix illustrated in part A of FIG. 27, the positions of elements having the value 1 are indicated by dots (“⋅”).

Part B of FIG. 27 illustrates processing that the demultiplexer 25 (FIG. 9) performs on an LDPC code of the transformed parity check matrix illustrated in part A of FIG. 27, that is, an LDPC code that has been subjected to parity interleaving.

In part B of FIG. 27, using a modulation scheme for mapping each symbol to one of 16 constellation points, such as 16APSK or 16QAM, code bits of the LDPC code that has been subjected to parity interleaving are written to four columns of the memory 31 in the demultiplexer 25 in a column direction.

The code bits written to the four columns of the memory 31 in the column direction are read in a row direction in units of 4 bits, and are mapped to one symbol.

In this case, 4 code bits B₀, B₁, B₂, and B₃, which are to be mapped to one symbol, may be code bits corresponding to is in an arbitrary row of the transformed parity check matrix illustrated in part A of FIG. 27. In this case, the variable nodes corresponding to the code bits B₀, B₁, B₂, and B₃ are connected to the same check node.

Accordingly, in a case where 4 code bits B₀, B₁, B₂, and B₃ of one symbol are code bits corresponding to is in an arbitrary row of the transformed parity check matrix, an erasure occurring in the symbol would make it difficult to determine an appropriate message for the same check node to which the variable nodes respectively corresponding to the code bits B₀, B₁, B₂, and B₃ are connected, resulting in deterioration of decoding performance.

Also for code rates other than a code rate of 3/4, a plurality of code bits corresponding to a plurality of variable nodes connected to the same check node may be mapped to one 16APSK or 16QAM symbol.

Accordingly, the column twist interleaver 24 performs column twist interleaving on the LDPC code that has been subjected to parity interleaving, which is supplied from the parity interleaver 23, to interleave code bits of the LDPC code so that a plurality of code bits corresponding to is in an arbitrary row of the transformed parity check matrix are not included in one symbol.

FIG. 28 is a diagram depicting column twist interleaving.

More specifically, FIG. 28 illustrates the memory 31 (FIGS. 22 and 23) of the demultiplexer 25.

As described with reference to FIG. 22, the memory 31 has a storage capacity to store N/(mb) bits in its column (vertical) direction and mb bits in its row (horizontal) direction, and includes mb columns. Then, the column twist interleaver 24 performs column twist interleaving by controlling a write start position from which the writing operation starts when a code bit of an LDPC code is written to the memory 31 in the column direction and is read from the memory 31 in the row direction.

More specifically, the column twist interleaver 24 appropriately changes a write start position with which the writing of a code bit starts in each of a plurality of columns so that a plurality of code bits read in the row direction, which are to be mapped to one symbol, does not match code bits corresponding to is in an arbitrary row of the transformed parity check matrix (That is, the column twist interleaver 24 reorders code bits of the LDPC code so that a plurality of code bits corresponding to is in an arbitrary row of the parity check matrix are not included in the same symbol).

Here, FIG. 28 illustrates an example configuration of the memory 31 in a case where the modulation scheme is 16APSK or 16QAM and the multiple b described with reference to FIG. 22 is 1. Accordingly, the number of bits m of the code bits of the LDPC code that are to be mapped to one symbol is 4, and the memory 31 includes 4 (=mb) columns.

The column twist interleaver 24 (instead of the demultiplexer 25 illustrated in FIG. 22) writes code bits of the LDPC code to the memory 31 (in the column direction) from the top to the bottom of each of the 4 columns of the memory 31, where the writing operation moves toward the right, starting from the leftmost column.

Further, when the writing of code bits up to the rightmost column is completed, the column twist interleaver 24 reads code bits from the memory 31 in the row direction, starting from the first row of all the columns of the memory 31, in units of 4 bits (i.e., mb bits), and outputs the read code bits as an LDPC code that has been subjected to column twist interleaving to the permutation unit 32 (FIGS. 22 and 23) of the demultiplexer 25.

In this regard, in the column twist interleaver 24, if the address of the first (or top) position of each column is represented by 0 and the addresses of the respective positions in the column direction are represented by integers arranged in ascending order, the write start position for the leftmost column is set to the position at the address 0, the write start position for the second column (from the left) is set to the position at the address 2, the write start position for the third column is set to the position at the address 4, and the write start position for the fourth column is set to the position of the address 7.

Note that, after writing code bits up to the bottom of the column for which the write start position is set to a position other than the position at the address 0, the column twist interleaver 24 returns to the first position (i.e., the position at the address 0), and writes code bits up to the position immediately before the write start position. The column twist interleaver 24 then performs writing to the subsequent (right) column.

The column twist interleaving operation described above may prevent a plurality of code bits corresponding to a plurality of variable nodes connected to the same check node for an LDPC code defined in DVB-T.2 and similar standards from being mapped to one symbol of 16APSK or 16QAM (i.e., from being included in the same symbol). Therefore, decoding performance can be improved in a communication path with an erasure.

FIG. 29 illustrates the number of columns of the memory 31 which is necessary for column twist interleaving, and the addresses of write start positions, in association with each modulation scheme, for an LDPC code having a code length N of 64800 and each of the 11 code rates, which is defined in the DVB-T.2 standard.

The multiple b is 1, and the number of bits m of one symbol is 2 when, for example, QPSK is employed as a modulation scheme. In this case, as illustrated in FIG. 29, the memory 31 has 2 columns for storing 2×1 (=mb) bits in its row direction, and stores 64800/(2×1) bits in its column direction.

Further, the write start position for the first column out of the 2 columns of the memory 31 is set to the position at the address 0, and the write start position for the second column is set to the position at the address 2.

The multiple b is 1 when, for example, one of the first to third permutation types illustrated in FIG. 22 is employed as the permutation type of the permutation processing of the demultiplexer 25 (FIG. 9).

The multiple b is 2, and the number of bits m of one symbol is 2 when, for example, QPSK is employed as a modulation scheme. In this case, as illustrated in FIG. 29, the memory 31 has 4 columns for storing 2×2 bits in its row direction, and stores 64800/(2×2) bits in its column direction.

Further, the write start position for the first column out of the 4 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 2, the write start position for the third column is set to the position at the address 4, and the write start position for the fourth column is set to the position at the address 7.

Note that the multiple b is 2 when, for example, the fourth permutation type illustrated in FIG. 23 is employed as the permutation type of the permutation processing of the demultiplexer 25 (FIG. 9).

The multiple b is 1, and the number of bits m of one symbol is 4 when, for example, 16QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 29, the memory 31 has 4 columns for storing 4×1 bits in its row direction, and stores 64800/(4×1) bits in its column direction.

Further, the write start position for the first column out of the 4 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 2, the write start position for the third column is set to the position at the address 4, and the write start position for the fourth column is set to the position at the address 7.

The multiple b is 2, and the number of bits m of one symbol is 4 when, for example, 16QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 29, the memory 31 has 8 columns for storing 4×2 bits in its row direction, and stores 64800/(4×2) bits in its column direction.

Further, the write start position for the first column out of the 8 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 0, the write start position for the third column is set to the position at the address 2, the write start position for the fourth column is set to the position at the address 4, the write start position for the fifth column is set to the position at the address 4, the write start position for the sixth column is set to the position at the address 5, the write start position for the seventh column is set to the position at the address 7, and the write start position for the eighth column is set to the position at the address 7.

The multiple b is 1, and the number of bits m of one symbol is 6 when, for example, 64QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 29, the memory 31 has 6 columns for storing 6×1 bits in its row direction, and stores 64800/(6×1) bits in its column direction.

Further, the write start position for the first column out of the 6 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 2, the write start position for the third column is set to the position at the address 5, the write start position for the fourth column is set to the position at the address 9, the write start position for the fifth column is set to the position at the address 10, and the write start position for the sixth column is set to the position at the address 13.

The multiple b is 2, and the number of bits m of one symbol is 6 when, for example, 64QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 29, the memory 31 has 12 columns for storing 6×2 bits in its row direction, and stores 64800/(6×2) bits in its column direction.

Further, the write start position for the first column out of the 12 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 0, the write start position for the third column is set to the position at the address 2, the write start position for the fourth column is set to the position at the address 2, the write start position for the fifth column is set to the position at the address 3, the write start position for the sixth column is set to the position at the address 4, the write start position for the seventh column is set to the position at the address 4, the write start position for the eighth column is set to the position at the address 5, the write start position for the ninth column is set to the position at the address 5, the write start position for the tenth column is set to the position at the address 7, the write start position for the eleventh column is set to the position at the address 8, and the write start position for the twelfth column is set to the position at the address 9.

The multiple b is 1, and the number of bits m of one symbol is 8 when, for example, 256QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 29, the memory 31 has 8 columns for storing 8×1 bits in its row direction, and stores 64800/(8×1) bits in its column direction.

Further, the write start position for the first column out of the 8 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 0, the write start position for the third column is set to the position at the address 2, the write start position for the fourth column is set to the position at the address 4, the write start position for the fifth column is set to the position at the address 4, the write start position for the sixth column is set to the position at the address 5, the write start position for the seventh column is set to the position at the address 7, and the write start position for the eighth column is set to the position at the address 7.

The multiple b is 2, and the number of bits m of one symbol is 8 when, for example, 256QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 29, the memory 31 has 16 columns for storing 8×2 bits in its row direction, and stores 64800/(8×2) bits in its column direction.

Further, the write start position for the first column out of the 16 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 2, the write start position for the third column is set to the position at the address 2, the write start position for the fourth column is set to the position at the address 2, the write start position for the fifth column is set to the position at the address 2, the write start position for the sixth column is set to the position at the address 3, the write start position for the seventh column is set to the position at the address 7, the write start position for the eighth column is set to the position at the address 15, the write start position for the ninth column is set to the position at the address 16, the write start position for the tenth column is set to the position at the address 20, the write start position for the eleventh column is set to the position at the address 22, the write start position for the twelfth column is set to the position at the address 22, the write start position for the thirteenth column is set to the position at the address 27, the write start position for the fourteenth column is set to the position at the address 27, the write start position for the fifteenth column is set to the position at the address 28, and the write start position for the sixteenth column is set to the position at the address 32.

The multiple b is 1, and the number of bits m of one symbol is 10 when, for example, 1024QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 29, the memory 31 has 10 columns for storing 10×1 bits in its row direction, and stores 64800/(10×1) bits in its column direction.

Further, the write start position for the first column out of the 10 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 3, the write start position for the third column is set to the position at the address 6, the write start position for the fourth column is set to the position at the address 8, the write start position for the fifth column is set to the position at the address 11, the write start position for the sixth column is set to the position at the address 13, the write start position for the seventh column is set to the position at the address 15, the write start position for the eighth column is set to the position at the address 17, the write start position for the ninth column is set to the position at the address 18, and the write start position for the tenth column is set to the position at the address 20.

The multiple b is 2, and the number of bits m of one symbol is 10 when, for example, 1024QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 29, the memory 31 has 20 columns for storing 10×2 bits in its row direction, and stores 64800/(10×2) bits in its column direction.

Further, the write start position for the first column out of the 20 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 1, the write start position for the third column is set to the position at the address 3, the write start position for the fourth column is set to the position at the address 4, the write start position for the fifth column is set to the position at the address 5, the write start position for the sixth column is set to the position at the address 6, the write start position for the seventh column is set to the position at the address 6, the write start position for the eighth column is set to the position at the address 9, the write start position for the ninth column is set to the position at the address 13, the write start position for the tenth column is set to the position at the address 14, the write start position for the eleventh column is set to the position at the address 14, the write start position for the twelfth column is set to the position at the address 16, the write start position for the thirteenth column is set to the position at the address 21, the write start position for the fourteenth column is set to the position at the address 21, the write start position for the fifteenth column is set to the position at the address 23, the write start position for the sixteenth column is set to the position at the address 25, the write start position for the seventeenth column is set to the position at the address 25, the write start position for the eighteenth column is set to the position at the address 26, the write start position for the nineteenth column is set to the position at the address 28, and the write start position for the twentieth column is set to the position at the address 30.

The multiple b is 1, and the number of bits m of one symbol is 12 when, for example, 4096QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 29, the memory 31 has 12 columns for storing 12×1 bits in its row direction, and stores 64800/(12×1) bits in its column direction.

Further, the write start position for the first column out of the 12 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 0, the write start position for the third column is set to the position at the address 2, the write start position for the fourth column is set to the position at the address 2, the write start position for the fifth column is set to the position at the address 3, the write start position for the sixth column is set to the position at the address 4, the write start position for the seventh column is set to the position at the address 4, the write start position for the eighth column is set to the position at the address 5, the write start position for the ninth column is set to the position at the address 5, the write start position for the tenth column is set to the position at the address 7, the write start position for the eleventh column is set to the position at the address 8, and the write start position for the twelfth column is set to the position at the address 9.

The multiple b is 2, and the number of bits m of one symbol is 12 when, for example, 4096QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 29, the memory 31 has 24 columns for storing 12×2 bits in its row direction, and stores 64800/(12×2) bits in its column direction.

Further, the write start position for the first column out of the 24 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 5, the write start position for the third column is set to the position at the address 8, the write start position for the fourth column is set to the position at the address 8, the write start position for the fifth column is set to the position at the address 8, the write start position for the sixth column is set to the position at the address 8, the write start position for the seventh column is set to the position at the address 10, the write start position for the eighth column is set to the position at the address 10, the write start position for the ninth column is set to the position at the address 10, the write start position for the tenth column is set to the position at the address 12, the write start position for the eleventh column is set to the position at the address 13, the write start position for the twelfth column is set to the position at the address 16, the write start position for the thirteenth column is set to the position at the address 17, the write start position for the fourteenth column is set to the position at the address 19, the write start position for the fifteenth column is set to the position at the address 21, the write start position for the sixteenth column is set to the position at the address 22, the write start position for the seventeenth column is set to the position at the address 23, the write start position for the eighteenth column is set to the position at the address 26, the write start position for the nineteenth column is set to the position at the address 37, the write start position for the twentieth column is set to the position at the address 39, the write start position for the twenty-first column is set to the position at the address 40, the write start position for the twenty-second column is set to the position at the address 41, the write start position for the twenty-third column is set to the position at the address 41, and the write start position for the twenty-fourth column is set to the position at the address 41.

FIG. 30 illustrates the number of columns of the memory 31 which is necessary for column twist interleaving, and the addresses of write start positions, in association with each modulation scheme, for an LDPC code having a code length N of 16200 and each of the 10 code rates, which is defined in the DVB-T.2 standard.

The multiple b is 1, and the number of bits m of one symbol is 2 when, for example, QPSK is employed as a modulation scheme. In this case, as illustrated in FIG. 30, the memory 31 has 2 columns for storing 2×1 bits in its row direction, and stores 16200/(2×1) bits in its column direction.

Further, the write start position for the first column out of the 2 columns of the memory 31 is set to the position at the address 0, and the write start position for the second column is set to the position at the address 0.

The multiple b is 2, and the number of bits m of one symbol is 2 when, for example, QPSK is employed as a modulation scheme. In this case, as illustrated in FIG. 30, the memory 31 has 4 columns for storing 2×2 bits in its row direction, and stores 16200/(2×2) bits in its column direction.

Further, the write start position for the first column out of the 4 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 2, the write start position for the third column is set to the position at the address 3, and the write start position for the fourth column is set to the position at the address 3.

The multiple b is 1, and the number of bits m of one symbol is 4 when, for example, 16QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 30, the memory 31 has 4 columns for storing 4×1 bits in its row direction, and stores 16200/(4×1) bits in its column direction.

Further, the write start position for the first column out of the 4 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 2, the write start position for the third column is set to the position at the address 3, and the write start position for the fourth column is set to the position at the address 3.

The multiple b is 2, and the number of bits m of one symbol is 4 when, for example, 16QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 30, the memory 31 has 8 columns for storing 4×2 bits in its row direction, and stores 16200/(4×2) bits in its column direction.

Further, the write start position for the first column out of the 8 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 0, the write start position for the third column is set to the position at the address 0, the write start position for the fourth column is set to the position at the address 1, the write start position for the fifth column is set to the position at the address 7, the write start position for the sixth column is set to the position at the address 20, the write start position for the seventh column is set to the position at the address 20, and the write start position for the eighth column is set to the position at the address 21.

The multiple b is 1, and the number of bits m of one symbol is 6 when, for example, 64QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 30, the memory 31 has 6 columns for storing 6×1 bits in its row direction, and stores 16200/(6×1) bits in its column direction.

Further, the write start position for the first column out of the 6 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 0, the write start position for the third column is set to the position at the address 2, the write start position for the fourth column is set to the position at the address 3, the write start position for the fifth column is set to the position at the address 7, and the write start position for the sixth column is set to the position at the address 7.

The multiple b is 2, and the number of bits m of one symbol is 6 when, for example, 64QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 30, the memory 31 has 12 columns for storing 6×2 bits in its row direction, and stores 16200/(6×2) bits in its column direction.

Further, the write start position for the first column out of the 12 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 0, the write start position for the third column is set to the position at the address 0, the write start position for the fourth column is set to the position at the address 2, the write start position for the fifth column is set to the position at the address 2, the write start position for the sixth column is set to the position at the address 2, the write start position for the seventh column is set to the position at the address 3, the write start position for the eighth column is set to the position at the address 3, the write start position for the ninth column is set to the position at the address 3, the write start position for the tenth column is set to the position at the address 6, the write start position for the eleventh column is set to the position at the address 7, and the write start position for the twelfth column is set to the position at the address 7.

The multiple b is 1, and the number of bits m of one symbol is 8 when, for example, 256QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 30, the memory 31 has 8 columns for storing 8×1 bits in its row direction, and stores 16200/(8×1) bits in its column direction.

Further, the write start position for the first column out of the 8 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 0, the write start position for the third column is set to the position at the address 0, the write start position for the fourth column is set to the position at the address 1, the write start position for the fifth column is set to the position at the address 7, the write start position for the sixth column is set to the position at the address 20, the write start position for the seventh column is set to the position at the address 20, and the write start position for the eighth column is set to the position at the address 21.

The multiple b is 1, and the number of bits m of one symbol is 10 when, for example, 1024QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 30, the memory 31 has 10 columns for storing 10×1 bits in its row direction, and stores 16200/(10×1) bits in its column direction.

Further, the write start position for the first column out of the 10 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 1, the write start position for the third column is set to the position at the address 2, the write start position for the fourth column is set to the position at the address 2, the write start position for the fifth column is set to the position at the address 3, the write start position for the sixth column is set to the position at the address 3, the write start position for the seventh column is set to the position at the address 4, the write start position for the eighth column is set to the position at the address 4, the write start position for the ninth column is set to the position at the address 5, and the write start position for the tenth column is set to the position at the address 7.

The multiple b is 2, and the number of bits m of one symbol is 10 when, for example, 1024QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 30, the memory 31 has 20 columns for storing 10×2 bits in its row direction, and stores 16200/(10×2) bits in its column direction.

Further, the write start position for the first column out of the 20 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 0, the write start position for the third column is set to the position at the address 0, the write start position for the fourth column is set to the position at the address 2, the write start position for the fifth column is set to the position at the address 2, the write start position for the sixth column is set to the position at the address 2, the write start position for the seventh column is set to the position at the address 2, the write start position for the eighth column is set to the position at the address 2, the write start position for the ninth column is set to the position at the address 5, the write start position for the tenth column is set to the position at the address 5, the write start position for the eleventh column is set to the position at the address 5, the write start position for the twelfth column is set to the position at the address 5, the write start position for the thirteenth column is set to the position at the address 5, the write start position for the fourteenth column is set to the position at the address 7, the write start position for the fifteenth column is set to the position at the address 7, the write start position for the sixteenth column is set to the position at the address 7, the write start position for the seventeenth column is set to the position at the address 7, the write start position for the eighteenth column is set to the position at the address 8, the write start position for the nineteenth column is set to the position at the address 8, and the write start position for the twentieth column is set to the position at the address 10.

The multiple b is 1, and the number of bits m of one symbol is 12 when, for example, 4096QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 30, the memory 31 has 12 columns for storing 12×1 bits in its row direction, and stores 16200/(12×1) bits in its column direction.

Further, the write start position for the first column out of the 12 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 0, the write start position for the third column is set to the position at the address 0, the write start position for the fourth column is set to the position at the address 2, the write start position for the fifth column is set to the position at the address 2, the write start position for the sixth column is set to the position at the address 2, the write start position for the seventh column is set to the position at the address 3, the write start position for the eighth column is set to the position at the address 3, the write start position for the ninth column is set to the position at the address 3, the write start position for the tenth column is set to the position at the address 6, the write start position for the eleventh column is set to the position at the address 7, and the write start position for the twelfth column is set to the position at the address 7.

The multiple b is 2, and the number of bits m of one symbol is 12 when, for example, 4096QAM is employed as a modulation scheme. In this case, as illustrated in FIG. 30, the memory 31 has 24 columns for storing 12×2 bits in its row direction, and stores 16200/(12×2) bits in its column direction.

Further, the write start position for the first column out of the 24 columns of the memory 31 is set to the position at the address 0, the write start position for the second column is set to the position at the address 0, the write start position for the third column is set to the position at the address 0, the write start position for the fourth column is set to the position at the address 0, the write start position for the fifth column is set to the position at the address 0, the write start position for the sixth column is set to the position at the address 0, the write start position for the seventh column is set to the position at the address 0, the write start position for the eighth column is set to the position at the address 1, the write start position for the ninth column is set to the position at the address 1, the write start position for the tenth column is set to the position at the address 1, the write start position for the eleventh column is set to the position at the address 2, the write start position for the twelfth column is set to the position at the address 2, the write start position for the thirteenth column is set to the position at the address 2, the write start position for the fourteenth column is set to the position at the address 3, the write start position for the fifteenth column is set to the position at the address 7, the write start position for the sixteenth column is set to the position at the address 9, the write start position for the seventeenth column is set to the position at the address 9, the write start position for the eighteenth column is set to the position at the address 9, the write start position for the nineteenth column is set to the position at the address 10, the write start position for the twentieth column is set to the position at the address 10, the write start position for the twenty-first column is set to the position at the address 10, the write start position for the twenty-second column is set to the position at the address 10, the write start position for the twenty-third column is set to the position at the address 10, and the write start position for the twenty-fourth column is set to the position at the address 11.

FIG. 31 is a flowchart depicting a process performed in the LDPC encoder 115, the bit interleaver 116, and the QAM encoder 117 illustrated in FIG. 8.

The LDPC encoder 115 waits for LDPC target data to be supplied from the BCH encoder 114. In step S101, the LDPC encoder 115 encodes the LDPC target data into an LDPC code, and supplies the LDPC code to the bit interleaver 116. Then, the process proceeds to step S102.

In step S102, the bit interleaver 116 performs bit interleaving on the LDPC code supplied from the LDPC encoder 115, and supplies a symbol obtained by symbolizing the LDPC code that has been subjected to bit interleaving, to the QAM encoder 117. Then, the process proceeds to step S103.

More specifically, in step S102, in the bit interleaver 116 (FIG. 9), the parity interleaver 23 performs parity interleaving on the LDPC code supplied from the LDPC encoder 115, and supplies the LDPC code that has been subjected to parity interleaving to the column twist interleaver 24.

The column twist interleaver 24 performs column twist interleaving on the LDPC code supplied from the parity interleaver 23, and supplies the resulting LDPC code to the demultiplexer 25.

The demultiplexer 25 performs permutation processing to permute the code bits of the LDPC code that has been subjected to column twist interleaving by the column twist interleaver 24 and to map the permuted code bits to symbol bits of a symbol (i.e., bits representing the symbol).

Here, the permutation processing of the demultiplexer 25 may be performed in accordance with any of the first to fourth permutation types illustrated in FIGS. 22 and 23, and may also be performed in accordance with a certain predetermined allocation rule to allocate code bits of an LDPC code to symbol bits representing a symbol.

The symbols obtained by the permutation processing performed by the demultiplexer 25 are supplied from the demultiplexer 25 to the QAM encoder 117.

In step S103, the QAM encoder 117 maps the symbols supplied from the demultiplexer 25 to constellation points defined by the modulation scheme for the orthogonal modulation to be performed by the QAM encoder 117, and then performs orthogonal modulation. The resulting data is supplied to the time interleaver 118.

As described above, parity interleaving and column twist interleaving may improve resistance to erasures or burst errors in a case where a plurality of code bits of an LDPC code are transmitted as one symbol.

Here, in FIG. 9, the parity interleaver 23 serving as a block configured to perform parity interleaving and the column twist interleaver 24 serving as a block configured to perform column twist interleaving are configured as separate units, for convenience of illustration. However, the parity interleaver 23 and the column twist interleaver 24 may be integrated into a single unit.

More specifically, both parity interleaving and column twist interleaving can be performed by writing and reading code bits to and from a memory, and can be represented by a matrix that converts an address at which a code bit is to be written i.e., a write address) to an address at which a code bit is to be read (i.e., a read address).

Accordingly, once a matrix obtained by multiplying a matrix representing parity interleaving and a matrix representing column twist interleaving is determined, an LDPC code that has been subjected to parity interleaving and then column twist interleaving can be obtained by converting code bits using the determined matrix.

Furthermore, the demultiplexer 25 in addition to the parity interleaver 23 and the column twist interleaver 24 may also be integrated into a single unit.

More specifically, the permutation processing performed in the demultiplexer 25 can also be represented by a matrix that converts a write address in the memory 31 at which an LDPC code is stored to a read address.

Accordingly, once a matrix obtained by multiplying a matrix representing parity interleaving, a matrix representing column twist interleaving, and a matrix representing permutation processing is determined, parity interleaving, column twist interleaving, and permutation processing can be performed in a batch way using the determined matrix.

Note that either parity interleaving or column twist interleaving may be performed, or neither of them may be performed. For example, as in the DVB-S.2 system, if the communication path 13 (FIG. 7) is a non-AWGN channel that does not much take into account burst errors, flutters, and so forth, such as a satellite link, none of parity interleaving and column twist interleaving may be performed.

Next, simulations for measuring error rates (bit error rates) that were performed on the transmitting device 11 illustrated in FIG. 8 will be described with reference to FIGS. 32 to 34.

The simulations were performed using a communication path with a flutter having a D/U of 0 dB.

FIG. 32 illustrates a model of a communication path employed in the simulations.

More specifically, part A of FIG. 32 illustrates a model of a flutter employed in the simulations.

Further, part B of FIG. 32 illustrates a model of a communication path having the flutter represented by the model illustrated in part A of FIG. 32.

Note that, in part B of FIG. 32, H represents the model of the flutter illustrated in part A of FIG. 32. In part B of FIG. 32, furthermore, N represents the ICI (Inter Carrier Interference). In the simulations, an expected value E[N²] of the power of the ICI was approximated by AWGN.

FIGS. 33 and 34 illustrate relationships between Doppler frequencies f_(d) of flutters and error rates obtained in the simulations.

Note that FIG. 33 illustrates relationships between error rates and Doppler frequencies f_(d) in a case where the modulation scheme is 16QAM, the code rate (r) is 3/4, and the permutation type is the first permutation type. FIG. 34 illustrates relationships between error rates and Doppler frequencies f_(d) in a case where the modulation scheme is 64QAM, the code rate (r) is 5/6, and the permutation type is the first permutation type.

In FIGS. 33 and 34, furthermore, bold lines indicate relationships between error rates and Doppler frequencies f_(d) in a case where parity interleaving, column twist interleaving, and permutation processing were all carried out, and thin lines indicate relationships between error rates and Doppler frequencies f_(d) in a case where only permutation processing out of parity interleaving, column twist interleaving, and permutation processing was carried out.

It can be seen from any of FIGS. 33 and 34 that the error-rate performance is improved (i.e., error rates are reduced) in the case where parity interleaving, column twist interleaving, and permutation processing were all carried out, compared to the case where only permutation processing was carried out.

[Example Configuration of LDPC Encoder 115]

FIG. 35 is a block diagram illustrating an example configuration of the LDPC encoder 115 illustrated in FIG. 8.

Note that the LDPC encoder 122 illustrated in FIG. 8 also has a similar configuration.

As described with reference to FIGS. 12 and 13, LDPC codes having two types of code lengths N of 64800 bits and 16200 bits are defined in the DVB-S.2 and similar standards.

In addition, 11 code rates, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 8/9, and 9/10, are defined for LDPC codes having a code length N of 64800 bits, and 10 code rates, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, and 8/9, are defined for LDPC codes having a code length N of 16200 bits (FIGS. 12 and 13).

The LDPC encoder 115 is capable of performing encoding (i.e., error correcting encoding) using, for example, the LDPC codes having code lengths N of 64800 bits and 16200 bits and the respective code rates, in accordance with the parity check matrix H prepared for each code length N and each code rate.

The LDPC encoder 115 includes an encoding processing unit 601 and a storage unit 602.

The encoding processing unit 601 includes a code rate setting unit 611, an initial value table read unit 612, a parity check matrix generation unit 613, an information bit read unit 614, an encoding parity computation unit 615, and a control unit 616. The encoding processing unit 601 performs LDPC encoding on the LDPC target data supplied to the LDPC encoder 115, and supplies the resulting LDPC code to the bit interleaver 116 (FIG. 8).

More specifically, the code rate setting unit 611 sets a code length N and a code rate of the LDPC code in accordance with, for example, an operation of an operator or the like.

The initial value table read unit 612 reads a parity check matrix initial value table, described below, corresponding to the code length N and code rate set by the code rate setting unit 611 from the storage unit 602.

The parity check matrix generation unit 613 generates a parity check matrix H on the basis of the parity check matrix initial value table read by the initial value table read unit 612, by arranging elements of 1 in an information matrix H_(A) having an information length K (=code length N−parity length M) corresponding to the code length N and code rate set by the code rate setting unit 611, in a column direction at intervals of 360 columns (i.e., the number of unit columns P of the cyclic structure). The parity check matrix H is stored in the storage unit 602.

The information bit read unit 614 reads (or extracts) information bits corresponding to the information length K from the LDPC target data supplied to the LDPC encoder 115.

The encoding parity computation unit 615 reads the parity check matrix H generated by the parity check matrix generation unit 613 from the storage unit 602, and generates a code word (i.e., an LDPC code) by calculating parity bits corresponding to the information bits read by the information bit read unit 614 in accordance with a certain formula by using the parity check matrix H.

The control unit 616 controls the blocks included in the encoding processing unit 601.

The storage unit 602 has stored therein a plurality of parity check matrix initial value tables and the like respectively corresponding to the plurality of code rates and the like illustrated in FIGS. 12 and 13 for the respective code lengths N such as 64800 bits and 16200 bits. In addition, the storage unit 602 temporarily stores data necessary for the processing of the encoding processing unit 601.

FIG. 36 is a flowchart depicting a process of the LDPC encoder 115 illustrated in FIG. 35.

In step S201, the code rate setting unit 611 determines (or sets) a code length N and a code rate r for LDPC encoding.

In step S202, the initial value table read unit 612 reads a predetermined parity check matrix initial value table corresponding to the code length N and code rate r determined by the code rate setting unit 611 from the storage unit 602.

In step S203, the parity check matrix generation unit 613 determines (or generates) a parity check matrix H of an LDPC code having the code length N and code rate r determined by the code rate setting unit 611 by using the parity check matrix initial value table read by the initial value table read unit 612 from the storage unit 602, and supplies the parity check matrix H to the storage unit 602 for storage.

In step S204, the information bit read unit 614 reads information bits of the information length K (=N×r) corresponding to the code length N and code rate r determined by the code rate setting unit 611 from the LDPC target data supplied to the LDPC encoder 115, and also reads the parity check matrix H determined by the parity check matrix generation unit 613 from the storage unit 602. Then, the information bit read unit 614 supplies the read information bits and parity check matrix H to the encoding parity computation unit 615.

In step S205, the encoding parity computation unit 615 sequentially computes parity bits of a code word c satisfying Expression (8) by using the information bits and the parity check matrix H supplied from the information bit read unit 614.

Hc ^(T)=0  (8)

In Expression (8), c denotes a row vector as a code word (i.e., LDPC code), and c^(T) denotes the transpose of the row vector c.

Here, as described above, if an information bit portion of the row vector c as the LDPC code (i.e., one code word) is represented by a row vector A and a parity bit portion is represented by a row vector T, the row vector c can be represented by the equation c=[A|T] using the row vector A corresponding to information bits and the row vector T corresponding to parity bits.

It is necessary for the parity check matrix H and the row vector c=[A|T] corresponding to the LDPC code to satisfy the equation Hc^(T)=0. The values of the elements of the row vector T corresponding to parity bits in the row vector c=[A|T] satisfying the equation Hc^(T)=0 can be sequentially determined by setting the elements in the respective rows of the column vector Hc^(T) in the equation Hc^(T)=0 to zero in order, starting from the element in the first row, in a case where the parity matrix H_(T) in the parity check matrix H=[H_(A)|H_(A)] has the stepwise structure illustrated in FIG. 11.

The encoding parity computation unit 615 determines parity bits T corresponding to the information bits A supplied from the information bit read unit 614, and outputs a code word c=[A|T], which is represented by the information bits A and the parity bits T, as a result of LDPC encoding of the information bits A.

Then, in step S206, the control unit 616 determines whether or not to terminate the LDPC encoding operation. If it is determined in step S206 that the LDPC encoding operation is not to be terminated, for example, if there is any LDPC target data to be subjected to LDPC encoding, the process returns to step S201 (or step S204), and the processing of steps S201 (or steps S204) to S206 is subsequently repeatedly performed.

Further, if it is determined in step S206 that the LDPC encoding operation is to be terminated, for example, if there is no LDPC target data to be subjected to LDPC encoding, the LDPC encoder 115 terminates the process.

As described above, parity check matrix initial value tables corresponding to the respective code lengths N and the respective code rates r are prepared, and the LDPC encoder 115 performs LDPC encoding with a certain code length N and a certain code rate r by using a parity check matrix H generated from the parity check matrix initial value table corresponding to the certain code length N and the certain code rate r.

[Example of Parity Check Matrix Initial Value Table]

A parity check matrix initial value table is a table showing the positions of elements of 1 in an information matrix H_(A) (FIG. 10) having an information length K corresponding to a code length N and code rate r of an LDPC code (i.e., an LDPC code defined by the parity check matrix H) in the parity check matrix H, in units of 360 columns (i.e., the number of unit columns P of the cyclic structure). A parity check matrix initial value table is created in advance for each of parity check matrices H having the respective code lengths N and the respective code rates r.

FIG. 37 is a diagram illustrating an example of a parity check matrix initial value table.

More specifically, FIG. 37 illustrates a parity check matrix initial value table for a parity check matrix H having a code length N of 16200 bits and a code rate (nominal code rate defined in DVB-T.2) r of 1/4, which is defined in the DVB-T.2 standard.

The parity check matrix generation unit 613 (FIG. 35) determines a parity check matrix H in the following way using the parity check matrix initial value table.

More specifically, FIG. 38 illustrates a method for determining a parity check matrix H from a parity check matrix initial value table.

Note that the parity check matrix initial value table illustrated in FIG. 38 is a parity check matrix initial value table for a parity check matrix H having a code length N of 16200 bits and a code rate r of 2/3, which is defined in the DVB-T.2 standard.

As described above, a parity check matrix initial value table is a table showing the positions of elements of 1 in an information matrix H_(A) (FIG. 10) having an information length K corresponding to a code length N and code rate r of an LDPC code in units of 360 columns (i.e., the number of unit columns P of the cyclic structure). In the i-th row of the parity check matrix initial value table, row numbers of elements of 1 in the {1+360×(i−1)}-th column of the parity check matrix H (i.e., row numbers in which the row number of the first row of the parity check matrix H is set to 0), the number of which is equal to the number of column weights assigned to the {1+360×(i−1)}-th column, are arranged.

Here, since the parity matrix H_(T) (FIG. 10) of the parity check matrix H, corresponding to the parity length M, is determined in the manner illustrated in FIG. 25, the information matrix H_(A) (FIG. 10) of the parity check matrix H, corresponding to the information length K, is determined using the parity check matrix initial value table.

The number of rows k+1 of the parity check matrix initial value table differs depending on the information length K.

A relationship given by Expression (9) is established between the information length K and the number of rows k+1 of the parity check matrix initial value table.

K=(k+1)×360  (9)

Here, in Expression (9), 360 is the number of unit columns P of the cyclic structure described with reference to FIG. 26.

In the parity check matrix initial value table illustrated in FIG. 38, 13 values are arranged in each of the first to third rows, and three values are arranged in each of the fourth to (k+1)-th row (in FIG. 38, the 30th row).

Accordingly, the column weights of the parity check matrix H determined from the parity check matrix initial value table illustrated in FIG. 38 are 13 for the first to {1+360×(3−1)−1}-th columns, and 3 for the {1+360×(3−1)}-th to K-th columns.

In the parity check matrix initial value table illustrated in FIG. 38, the first row shows 0, 2084, 1613, 1548, 1286, 1460, 3196, 4297, 2481, 3369, 3451, 4620, and 2622, indicating that the elements of the rows with the row numbers 0, 2084, 1613, 1548, 1286, 1460, 3196, 4297, 2481, 3369, 3451, 4620, and 2622 in the first column of the parity check matrix H are 1 (and that the other elements are 0).

In the parity check matrix initial value table illustrated in FIG. 38, furthermore, the second row shows 1, 122, 1516, 3448, 2880, 1407, 1847, 3799, 3529, 373, 971, 4358, and 3108, indicating that the elements of the rows with the row numbers 1, 122, 1516, 3448, 2880, 1407, 1847, 3799, 3529, 373, 971, 4358, and 3108 in the 361st (=1+360×(2−1)) column of the parity check matrix H are 1.

In the manner described above, a parity check matrix initial value table shows the positions of elements of 1 in an information matrix H_(A) of a parity check matrix H in units of 360 columns.

The elements in the columns other than the {1+360×(i−1)}-th column of the parity check matrix H, that is, the elements in the {2+360×(i−1)}-th to (360×i)-th columns, are arranged by cyclically shifting the elements of 1 in the {1+360×(i−1)}-th column, which are defined using the parity check matrix initial value table, downward (i.e., downward along the columns) in a periodic manner in accordance with the parity length M.

More specifically, for example, the elements in the {2+360×(i−1)}-th column are obtained by cyclically shifting the elements in the {1+360×(i−1)}-th column downward by M/360 (=q). The elements in the subsequent {3+360×(i−1)}-th column are obtained by cyclically shifting the elements in the {1+360×(i−1)}-th column downward by 2×M/360 (=2×q) (i.e., by cyclically shifting the elements in the {2+360×(i−1)}-th column downward by M/360 (=q)).

It is assumed now that the value in the i-th row (i.e., the i-th row from the top) and the j-th column (i.e., the j-th column from the left) of a parity check matrix initial value table is represented by h_(i,j), and the row number of the j-th element of 1 in the w-th column of a parity check matrix H is represented by H_(w-j). In this case, the row number H_(w-j) of an element of 1 in the w-th column, which is a column other than the {1+360×(i−1)}-th column of the parity check matrix H, can be determined using Expression (10).

H _(w-j)=mod{h _(i,j)+mod((w−1),P)×q,M)   (10)

Here, mod(x, y) represents the remainder after division of x by y.

In addition, P denotes the number of unit columns of cyclic structure, described above, and is, for example, 360 in the DVB-S.2, DVB-T.2, and DVB-C.2 standards, as described above. Further, q denotes the value M/360 that is obtained by dividing the parity length M by the number of unit columns P of the cyclic structure (=360).

The parity check matrix generation unit 613 (FIG. 35) specifies a row number of an element of 1 in the {1+360×(i−1)}-th column of the parity check matrix H by using the parity check matrix initial value table.

The parity check matrix generation unit 613 (FIG. 35) further determines the row number H_(w-j) of an element of 1 in the w-th column, which is a column other than the {1+360×(i−1)}-th column of the parity check matrix H, in accordance with Expression (10), and generates a parity check matrix H whose elements corresponding to the row numbers obtained in the way described above are 1.

[New LDPC Codes]

Incidentally, there has been a demand for proposing an improved version (hereinafter also referred to as “DVB-Sx”) of the DVB-S.2 standard.

In the CfT (Call for Technology), which was submitted in the meeting for DVB-Sx standardization, a certain number of ModCods (which are combinations of modulation schemes (Modulation) and LDPC codes (Code)) are demanded for each range of C/N (Carrier to Noise Ratio) (SNR (Signal to Noise Ratio)) in accordance with use case.

More specifically, in the CfT, the first request is to prepare 20 ModCods for a C/N range of 7 dB from 5 dB to 12 dB for DTH (Direct To Home) use.

In the CfT, additionally, the second request is to prepare 22 ModCods for a C/N range of 12 dB from 12 dB to 24 dB, the third request is to prepare 12 ModCods for a C/N range of 8 dB from −3 dB to 5 dB, and the fourth request is to prepare 5 ModCods for a C/N range of 7 dB from −10 dB to −3 dB.

In the CfT, furthermore, it is also requested that the FER (Frame Error Rate) for the ModCods in the first to fourth requests be approximately 10⁻⁵ (or less).

Note that, in the CfT, the first request has a priority of “1”, which is the highest, whereas the second to fourth requests have a priority of “2”, which is lower than the priority of the first request.

Accordingly, the present technology provides (a parity check matrix of) an LDPC code capable of satisfying at least the first request having the highest priority in the CfT, as a new LDPC code.

FIG. 39 illustrates BER/FER curves for LDPC codes having a code length N of 64k bits and 11 code rates, which are defined in the DVB-S.2, in a case where QPSK is employed as a modulation scheme.

In FIG. 39, the horizontal axis represents E_(s)/N₀ (the ratio of the signal power per symbol to the noise power) corresponding to the C/N, and the vertical axis represents FER/BER. Note that, in FIG. 39, solid lines indicate FERs, and dotted lines indicate BERs (Bit Error Rates).

In FIG. 39, FER (BER) curves for LDPC codes having a code length N of 64k bits and 11 code rates, which are defined in the DVB-S.2 standard, are plotted for an E_(s)/N₀ range of 10 dB in a case where QPSK is employed as a modulation scheme.

More specifically, in FIG. 39, 11 FER curves for ModCods for which the modulation scheme is fixed to QPSK are drawn for an E_(s)/N₀ range of approximately 10 dB from approximately −3 dB to approximately 7 dB.

Accordingly, for LDPC codes having a code length N of 64k bits and 11 code rates, which are defined in the DVB-S.2 standard, the interval between FER curves for ModCods on average (hereinafter also referred to as an “average interval”) is approximately 1 dB (≅10 dB/(10−1)).

In contrast, since the first request in the CfT requests that 20 ModCods be prepared for an E_(s)/N₀ (C/N) range of 7 dB, the average interval between FER curves for ModCods is approximately 0.3 dB (≅7 dB/(20−1)).

In a case where the modulation scheme is fixed to one type such as QPSK, LDPC codes with code rates, the number of which is approximately three times (≅1 dB/0.3 dB) the 11 code rates, or approximately 30 code rates, would be sufficient to ensure sufficient room to obtain ModCods having an average interval of 0.3 dB which meets the first request in the CfT, compared to the case of DVB-S.2 in which ModCods having an average interval of approximately 1 dB are obtained using LDPC codes with the 11 code rates.

In the present technology, accordingly, LDPC codes having a code length of 64k and code rates of i/30 (where i is a positive integer less than 30) are prepared as LDPC codes having code rates for which approximately 30 code rates are readily settable, and are provided as new LDPC codes which meet at least the first request having the highest priority in the CfT.

It is to be noted that parity matrices H_(T) of parity check matrices H of the new LDPC codes have a stepwise structure (FIG. 11), similarly to an LDPC code defined in the DVB-S.2 standard, in terms of keeping compatibility with DVB-S.2 as much as possible.

In addition, similarly to an LDPC code defined in the DVB-S.2 standard, information matrices H_(A) of parity check matrices H of the new LDPC codes have a cyclic structure, where the number of unit columns P of the cyclic structure is also 360.

FIGS. 40 to 106 are diagrams illustrating an example of parity check matrix initial value tables for new LDPC codes having a code length N of 64k bits and code rates of i/30, as described above.

Here, the new LDPC codes are LDPC codes whose code rates are represented by i/30, and therefore include LDPC codes having up to 29 code rates, 1/30, 2/30, 3/30, . . . , 28/30, and 29/30.

However, an LDPC code with a code rate of 1/30 may be used in a limited fashion in terms of efficiency. In addition, an LDPC code with a code rate of 29/30 may be used in a limited fashion in terms of error rate (BER/FER).

For the reason described above, among LDPC codes with 29 code rates, namely, code rates of 1/30 to 29/30, one or both of an LDPC code with a code rate of 1/30 and an LDPC code with a code rate of 29/30 can be configured not to be used as new LDPC codes.

Herein, LDPC codes with 28 code rates, for example, LDPC codes with code rates of 2/30 to 29/30 among code rates of 1/30 to 29/30, are used as new LDPC codes, and parity check matrix initial value tables for parity check matrices H of the new LDPC codes will be given hereinbelow.

FIG. 40 illustrates a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 2/30.

FIG. 41 illustrates a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 3/30.

FIG. 42 illustrates a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 4/30.

FIG. 43 illustrates a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 5/30.

FIG. 44 illustrates a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 6/30.

FIG. 45 illustrates a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 7/30.

FIGS. 46 and 47 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 8/30.

FIGS. 48 and 49 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 9/30.

FIGS. 50 and 51 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 10/30.

FIGS. 52 and 53 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 11/30.

FIGS. 54 and 55 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 12/30.

FIGS. 56 and 57 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 13/30.

FIGS. 58 and 59 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 14/30.

FIGS. 60 and 61 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 15/30.

FIGS. 62, 63, and 64 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 16/30.

FIGS. 65, 66, and 67 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 17/30.

FIGS. 68, 69, and 70 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 18/30.

FIGS. 71, 72, and 73 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 19/30.

FIGS. 74, 75, and 76 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 20/30.

FIGS. 77, 78, and 79 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 21/30.

FIGS. 80, 81, and 82 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 22/30.

FIGS. 83, 84, and 85 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 23/30.

FIGS. 86, 87, and 88 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 24/30.

FIGS. 89, 90, and 91 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 25/30.

FIGS. 92, 93, and 94 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 26/30.

FIGS. 95, 96, 97, and 98 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 27/30.

FIGS. 99, 100, 101, and 102 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 28/30.

FIGS. 103, 104, 105, and 106 illustrate a parity check matrix initial value table for a parity check matrix H of an LDPC code having a code length N of 64k bits and a code rate r of 29/30.

The LDPC encoder 115 (FIGS. 8 and 35) is capable of performing encoding on a (new) LDPC code having a code length N of 64k bits and any of 28 code rates r of 2/30 to 29/30 by using a parity check matrix H determined from one of the parity check matrix initial value tables illustrated in FIGS. 40 to 106.

In the illustrated example, the storage unit 602 of the LDPC encoder 115 (FIG. 8) stores the parity check matrix initial value tables illustrated in FIGS. 40 to 106.

It is to be noted that not all the LDPC codes with 28 code rates r of 2/30 to 29/30 (which are determined from the parity check matrix initial value tables) illustrated in FIGS. 40 to 106 may be used as new LDPC. That is, an LDPC code or codes with any one or more code rates among the LDPC codes with 28 code rates r of 2/30 to 29/30 illustrated in FIGS. 40 to 106 may be employed as a new LDPC code or codes.

LDPC codes obtained using parity check matrices H determined from the parity check matrix initial value tables illustrated in FIGS. 40 to 106 may be high-performance LDPC codes.

The term “high-performance LDPC code”, as used herein, refers to an LDPC code obtained from an appropriate parity check matrix H.

Furthermore, the term “appropriate parity check matrix H” refers to a parity check matrix satisfying a certain condition in which the BER (and FER) is (or are) reduced when an LDPC code obtained from a parity check matrix H is transmitted with a low E_(s)/N₀ or E_(b)/N_(o) (which is the ratio of the signal power per bit to the noise power).

An appropriate parity check matrix H may be determined through simulations for measuring BERs when, for example, LDPC codes obtained from various parity check matrices satisfying a certain condition are transmitted with a low E_(s)/N_(o).

Examples of the certain condition that an appropriate parity check matrix H is to satisfy include a condition that analysis results obtained using an analytical technique for the performance evaluation of codes, called density evolution, are good, and a condition that a loop of elements of 1, called cycle 4, does not exist.

Here, it is well established that a concentration of elements of 1, like cycle 4, in an information matrix H_(A) will reduce the decoding performance of an LDPC code. Thus, the absence of cycle 4 is demanded as a certain condition that an appropriate parity check matrix H is to satisfy.

Note that the certain condition that an appropriate parity check matrix H is to satisfy may be determined, as desired, in terms of various factors such as improved decoding performance of an LDPC code and easy (or simplified) decoding processing of an LDPC code.

FIGS. 107 and 108 are diagrams depicting density evolution through which analysis results are obtained, as a certain condition that an appropriate parity check matrix H is to satisfy.

Density evolution is a code analysis technique for calculating an expected value of error probability for the set of all LDPC codes (“ensemble”) whose code length N, which is characterized by a degree sequence described below, is infinite (∞).

For example, if a noise variance increases from zero in an AWGN channel, the expected value of error probability for a certain ensemble is initially zero, and becomes non-zero if the noise variance is greater than or equal to a certain threshold.

In the density evolution method, it can be determined whether the ensemble performance (i.e., the appropriateness of a parity check matrix) is good or not, by comparing noise variance thresholds (hereinafter also referred to as “performance thresholds”) over which the expected values of error probability for ensembles become non-zero.

Note that the general performance of a specific LDPC code can be predicted by determining an ensemble including the LDPC code and performing density evolution on the ensemble.

Accordingly, once an ensemble with good performance is found, an LDPC code with good performance may be found from among the LDPC codes included in the ensemble.

Here, the degree sequence, described above, represents the ratio of variable nodes or check nodes with a weight of each value to the code length N of an LDPC code.

For example, a regular (3,6) LDPC code with a code rate of 1/2 belongs to an ensemble characterized by a degree sequence indicating that the weight (column weight) for all the variable nodes is 3 and the weight (row weight) for all the check nodes is 6.

FIG. 107 illustrates a Tanner graph of the above-described ensemble.

The Tanner graph illustrated in FIG. 107 includes N variable nodes indicated by circles (“◯”) in FIG. 107, the number of which is equal to the code length N, and N/2 check nodes indicated by squares (“□”) in FIG. 107, the number of which is equal to a value obtained by multiplying the code length N by the code rate 1/2.

Three edges, the number of which is equal to the column weight, are connected to each variable node. Therefore, 3N edges in total are connected to the N variable nodes.

In addition, six edges, the number of which is equal to the row weight, are connected to each check node. Therefore, 3N edges in total are connected to the N/2 check nodes.

In the Tanner graph illustrated in FIG. 107, one interleaver is also included.

The interleaver randomly reorders the 3N edges connected to the N variable nodes, and connects each of the reordered edges to one of the 3N edges connected to the N/2 check nodes.

There are (3N)! (=(3N)×(3N−1)× . . . ×1) reordering patterns in which the interleaver reorders the 3N edges connected to the N variable nodes. Accordingly, an ensemble characterized by a degree sequence indicating that the weight for all the variable nodes is 3 and the weight for all the check nodes is 6 is the set of (3N)! LDPC codes.

In a simulation for determining an LDPC code with good performance (i.e., an appropriate parity check matrix), a multi-edge type ensemble was used in density evolution.

In the multi-edge type, an interleaver through which edges connected to variable nodes and edges connected to check nodes extend is divided into a plurality of pieces (multi-edge), which may allow more accurate characterization of an ensemble.

FIG. 108 illustrates an example of a Tanner graph of a multi-edge type ensemble.

In the Tanner graph illustrated in FIG. 108, two interleavers, namely, a first interleaver and a second interleaver, are included.

In addition, the Tanner graph illustrated in FIG. 108 includes v1 variable nodes each having one edge connected to the first interleaver and zero edges connected to the second interleaver, v2 variable nodes each having one edge connected to the first interleaver and two edges connected to the second interleaver, and v3 variable nodes each having zero edges connected to the first interleaver and two edges connected to the second interleaver.

The Tanner graph illustrated in FIG. 108 further includes c1 check nodes each having two edges connected to the first interleaver and zero edges connected to the second interleaver, c2 check nodes each having two edges connected to the first interleaver and two edges connected to the second interleaver, and c3 check nodes each having zero edges connected to the first interleaver and three edges connected to the second interleaver.

Here, density evolution and an implementation thereof are described in, for example, “On the Design of Low-Density Parity-Check Codes within 0.0045 dB of the Shannon Limit”, S. Y. Chung, G. D. Forney, T. J. Richardson, R. Urbanke, IEEE Communications Leggers, VOL. 5, NO. 2, February 2001.

In a simulation for determining (a parity check matrix initial value table of) a new LDPC code, an ensemble for which the performance threshold, which is E_(b)/N₀ (which is the ratio of the signal power per bit to the noise power) at which a BER begins to drop (i.e., decreases), is less than or equal to a certain value was found using multi-edge type density evolution, and an LDPC code that reduces a BER in a plurality of modulation schemes used in DVB-S.2 and the like, such as QPSK, was selected as an LDPC code with good performance from among the LDPC codes belonging to the ensemble.

The parity check matrix initial value tables of the new LDPC codes described above are parity check matrix initial value tables of LDPC codes having a code length N of 64k bits, which are determined through the simulations described above.

FIG. 109 is a diagram illustrating minimum cycle lengths and performance thresholds for parity check matrices H which are determined from parity check matrix initial value tables of new LDPC codes having a code length N of 64k bits and 28 code rates of 2/30 to 29/30 illustrated in FIGS. 40 to 106.

Here, a minimum cycle length (or girth) is a minimum value of the length (loop length) of a loop composed of elements of 1 in a parity check matrix H.

Cycle 4 (a loop of elements of 1, with a loop length of 4) does not exist in a parity check matrix H determined from a parity check matrix initial value table of a new LDPC code.

In addition, as the code rate r decreases, the redundancy of an LDPC code increases. Thus, the performance threshold tends to be improved (i.e., decrease) as the code rate r decreases.

FIG. 110 is a diagram depicting a parity check matrix H (hereinafter also referred to as a “parity check matrix H of a new LDPC code”) (determined from each of the parity check matrix initial value tables) illustrated in FIGS. 40 to 106.

The parity check matrix H of the new LDPC code has a column weight X for KX columns, starting with the first column, a column weight of Y1 for the subsequent KY1 columns, a column weight of Y2 for the subsequent KY2 columns, a column weight of 2 for the subsequent (M−1) columns, and a column weight of 1 for the last column.

Here, the sum of columns given by KX+KY1+KY2+M−1+1 equals the code length N=64800 bits.

FIG. 111 is a diagram illustrating the numbers of columns KX, KY1, KY2, and M, and the column weights X, Y1, and Y2 illustrated in FIG. 110 for the respective code rates r of the new LDPC codes.

In a parity check matrix H of a new LDPC code having a code length N of 64k, similarly to the parity check matrix described with reference to FIGS. 12 and 13, the column weight tends to increase as the ordinal number of the columns of the parity check matrix H decreases (i.e., as the column comes closer to the left end of the parity check matrix H). Accordingly, robustness to errors (or resistance to errors) tends to increase as the ordinal number of the code bits of a new LDPC code decreases (i.e., the first code bit tends to be the most robust to errors).

It is noted that the amount of shift q used in cyclic shifting which is performed to determine a parity check matrix from a parity check matrix initial value table of a new LDPC code having a code length N of 64k in the way described with reference to FIG. 38 is represented by the equation q=M/P=M/360.

Accordingly, the amounts of shift for new LDPC codes with code rates of 2/30, 3/30, 4/30, 5/30, 6/30, 7/30, 8/30, 9/30, 10/30, 11/30, 12/30, 13/30, 14/30, 15/30, 16/30, 17/30, 18/30, 19/30, 20/30, 21/30, 22/30, 23/30, 24/30, 25/30, 26/30, 27/30, 28/30, and 29/30 are 168, 162, 156, 150, 144, 138, 132, 126, 120, 114, 108, 102, 96, 90, 84, 78, 72, 66, 60, 54, 48, 42, 36, 30, 24, 18, 12, and 6, respectively.

FIGS. 112, 113, and 114 are diagrams illustrating simulated BERs/FERs for the new LDPC codes illustrated in FIGS. 40 to 106.

The simulations were based on the assumption of an AWGN communication path (or channel), in which BPSK was employed as a modulation scheme and the number of times of repetitive decoding C(it) was 50.

In FIGS. 112, 113, and 114, the horizontal axis represents E_(s)/N₀, and the vertical axis represents BER/FER. Note that solid lines indicate BERs and dotted lines indicate FERs.

In FIGS. 112 to 114, FER (BER) curves for the respective new LDPC codes with 28 code rates of 2/30 to 29/30 exhibit FERs less than or equal to 10⁻⁵ for an E_(s)/N₀ range of (approximately) 15 dB from (substantially)−10 dB to 5 dB.

In the simulations, 28 ModCods having an FER less than or equal to 10⁻⁵ for an E_(s)/N₀ range of 15 dB from −10 dB to 5 dB can be set. Accordingly, 20 or more ModCods having an FER less than or equal to 10⁻⁵ for a range of 7 dB from 5 dB to 12 dB can be sufficiently predicted to be set by taking into account various modulation schemes other than BPSK used in the simulations, such as QPSK, 8PSK, 16APSK, 32APSK, 16QAM, 32QAM, and 64QAM.

Thus, it is possible to provide an LDPC code having good error-rate performance, meeting the first request in the CfT.

In addition, referring to FIGS. 112 to 114, most of FER (BER) curves for new LDPC codes are drawn at almost equal intervals less than 1 dB for each of low-, intermediate-, and high-code-rate groups. Accordingly, the new LDPC codes may provide broadcasters that broadcast programs using the transmitting device 11 with an advantage in facilitating selection of code rates to be used for broadcasting in accordance with the state of channels (i.e., the communication path 13).

Note that, in the simulations for determining the BER/FER curves illustrated in FIGS. 112 to 114, BCH encoding was performed on information, and the resulting BCH codes underwent LDPC encoding.

FIG. 115 includes diagrams depicting BCH encoding which was used in the simulations.

More specifically, part A of FIG. 115 is a diagram illustrating parameters of BCH encoding that is performed prior to the LDPC encoding into an LDPC code of 64k, which is defined in the DVB-S.2 standard.

In DVB-S.2, 192, 160, or 128 redundancy bits are added in accordance with the code rate of an LDPC code, thereby providing BCH encoding capable of 12-, 10-, or 8-bit error correction.

Part B of FIG. 115 is a diagram illustrating parameters of BCH encoding which were used in the simulations.

In the simulations, similarly to the case of DVB-S.2, BCH encoding capable of 12-, 10-, or 8-bit error correction was performed by addition of 192, 160, or 128 redundancy bits in accordance with the code rate of an LDPC code.

[Example Configuration of Receiving Device 12]

FIG. 116 is a block diagram illustrating an example configuration of the receiving device 12 illustrated in FIG. 7.

An OFDM processing unit (OFDM operation) 151 receives an OFDM signal from the transmitting device 11 (FIG. 7), and performs signal processing on the OFDM signal. The data (i.e., symbols) obtained through signal processing performed by the OFDM processing unit 151 is supplied to a frame management unit (Frame Management) 152.

The frame management unit 152 performs processing (frame interpretation) of a frame including the symbols supplied from the OFDM processing unit 151 to obtain symbols of target data and symbols of control data, and supplies the symbols of the target data and the symbols of the control data to frequency deinterleavers 161 and 153, respectively.

The frequency deinterleaver 153 performs frequency deinterleaving on the symbols supplied from the frame management unit 152 in units of symbols, and supplies the resulting symbols to a QAM decoder 154.

The QAM decoder 154 demaps the symbols (i.e., symbols mapped to constellation points) supplied from the frequency deinterleaver 153 (i.e., decodes the constellation points) for orthogonal demodulation, and supplies the resulting data (i.e., an LDPC code) to an LDPC decoder 155.

The LDPC decoder 155 performs LDPC decoding on the LDPC code supplied from the QAM decoder 154, and supplies the resulting LDPC target data (in the illustrated example, a BCH code) to a BCH decoder 156.

The BCH decoder 156 performs BCH decoding on the LDPC target data supplied from the LDPC decoder 155, and outputs the resulting control data (signalling).

On the other hand, the frequency deinterleaver 161 performs frequency deinterleaving on the symbols supplied from the frame management unit 152 in units of symbols, and supplies the resulting symbols to an MISO/MIMO decoder 162.

The MISO/MIMO decoder 162 performs space-time decoding on the data (i.e., symbols) supplied from the frequency deinterleaver 161, and supplies the resulting data to a time deinterleaver 163.

The time deinterleaver 163 performs time deinterleaving on the data (i.e., symbols) supplied from the MISO/MIMO decoder 162 in units of symbols, and supplies the resulting data to a QAM decoder 164.

The QAM decoder 164 demaps the symbols (i.e., symbols mapped to constellation points) supplied from the time deinterleaver 163 (i.e., decodes the constellation points) for orthogonal demodulation, and supplies the resulting data (i.e., symbols) to a bit deinterleaver 165.

The bit deinterleaver 165 performs bit deinterleaving on the data (i.e., symbols) supplied from the QAM decoder 164, and supplies the resulting LDPC code to an LDPC decoder 166.

The LDPC decoder 166 performs LDPC decoding on the LDPC code supplied from the bit deinterleaver 165, and supplies the resulting LDPC target data (in the illustrated example, a BCH code) to a BCH decoder 167.

The BCH decoder 167 performs BCH decoding on the LDPC target data supplied from the LDPC decoder 155, and supplies the resulting data to a BB descrambler 168.

The BB descrambler 168 performs BB descrambling on the data supplied from the BCH decoder 167, and supplies the resulting data to a null deletion unit (Null Deletion) 169.

The null deletion unit 169 deletes the null added by the padder 112 illustrated in FIG. 8, from the data supplied from the BB descrambler 168, and supplies the resulting data to a demultiplexer 170.

The demultiplexer 170 separates one or more streams (target data) multiplexed in the data supplied from the null deletion unit 169, performs necessary processing, and outputs the resulting data as output streams.

Note that the receiving device 12 may be configured without including some of the blocks illustrated in FIG. 116. More specifically, for example, if the transmitting device 11 (FIG. 8) is configured without including the time interleaver 118, the MISO/MIMO encoder 119, the frequency interleaver 120, and the frequency interleaver 124, the receiving device 12 may be configured without including the time deinterleaver 163, the MISO/MIMO decoder 162, the frequency deinterleaver 161, and the frequency deinterleaver 153, which are the blocks corresponding to the time interleaver 118, the MISO/MIMO encoder 119, the frequency interleaver 120, and the frequency interleaver 124 of the transmitting device 11, respectively.

FIG. 117 is a block diagram illustrating an example configuration of the bit deinterleaver 165 illustrated in FIG. 116.

The bit deinterleaver 165 includes a multiplexer (MUX) 54 and a column twist deinterleaver 55, and performs (bit) deinterleaving on the symbol bits of the symbols supplied from the QAM decoder 164 (FIG. 116).

More specifically, the multiplexer 54 performs inverse permutation processing (which is the inverse of permutation processing), corresponding to the permutation processing performed by the demultiplexer 25 illustrated in FIG. 9, on the symbol bits of the symbols supplied from the QAM decoder 164. That is, the multiplexer 54 performs inverse permutation processing to restore the positions of the code bits (i.e., symbol bits) of the LDPC code permuted through the permutation processing to the original positions, and supplies the resulting LDPC code to the column twist deinterleaver 55.

The column twist deinterleaver 55 performs column twist deinterleaving (which is the inverse of column twist interleaving), corresponding to column twist interleaving as the reordering processing performed by the column twist interleaver 24 illustrated in FIG. 9, on the LDPC code supplied from the multiplexer 54. That is, the column twist deinterleaver 55 performs inverse reordering processing, for example, column twist deinterleaving, to restore the code bits of the LDPC code whose order has been changed through column twist interleaving as reordering processing to the original order.

Specifically, the column twist deinterleaver 55 performs column twist deinterleaving by writing and reading the code bits of the LDPC code to and from a memory for deinterleaving which has a configuration similar to that of the memory 31 illustrated in, typically, FIG. 28.

However, the column twist deinterleaver 55 writes code bits to the memory for deinterleaving in its row direction by using, as a write address, the read address at which a code bit has been read from the memory 31. In addition, the column twist deinterleaver 55 reads code bits from the memory for deinterleaving in its column direction by using, as a read address, the write address at which a code bit has been written to the memory 31.

The LDPC code obtained as a result of column twist deinterleaving is supplied from the column twist deinterleaver 55 to the LDPC decoder 166.

Here, if the LDPC code supplied from the QAM decoder 164 to the bit deinterleaver 165 has been subjected to parity interleaving, column twist interleaving, and permutation processing, the bit deinterleaver 165 may perform all of the inverse operations, namely, parity deinterleaving corresponding to parity interleaving (which is the inverse of parity interleaving operation, i.e., parity deinterleaving for restoring the code bits of the LDPC code whose order has been changed through parity interleaving to the original order), inverse permutation processing corresponding to permutation processing, and column twist deinterleaving corresponding to column twist interleaving.

In the bit deinterleaver 165 illustrated in FIG. 117, however, parity deinterleaving is not performed because the bit deinterleaver 165 does not include a block configured to perform parity deinterleaving corresponding to parity interleaving although it includes the multiplexer 54 that performs inverse permutation processing corresponding to permutation processing and the column twist deinterleaver 55 that performs column twist deinterleaving corresponding to column twist interleaving.

Accordingly, the LDPC code on which inverse permutation processing and column twist deinterleaving have been performed but parity deinterleaving has not been performed is supplied from (the column twist deinterleaver 55 of) the bit deinterleaver 165 to the LDPC decoder 166.

The LDPC decoder 166 performs LDPC decoding on the LDPC code supplied from the bit deinterleaver 165 by using a transformed parity check matrix obtained by performing at least column permutation corresponding to parity interleaving on the parity check matrix H that the LDPC encoder 115 illustrated in FIG. 8 has used for LDPC encoding, and outputs the resulting data as a result of decoding the LDPC target data.

FIG. 118 is a flowchart depicting a process performed by the QAM decoder 164, the bit deinterleaver 165, and the LDPC decoder 166 illustrated in FIG. 117.

In step S111, the QAM decoder 164 demaps the symbols (i.e., symbols mapped to constellation points) supplied from the time deinterleaver 163 for orthogonal demodulation, and supplies the resulting data to the bit deinterleaver 165. Then, the process proceeds to step S112.

In step S112, the bit deinterleaver 165 performs deinterleaving (i.e., bit deinterleaving) on the symbol bits of the symbols supplied from the QAM decoder 164. Then, the process proceeds to step S113.

More specifically, in step S112, the multiplexer 54 in the bit deinterleaver 165 performs inverse permutation processing on the symbol bits of the symbols supplied from the QAM decoder 164, and supplies the code bits of the resulting LDPC code to the column twist deinterleaver 55.

The column twist deinterleaver 55 performs column twist deinterleaving on the LDPC code supplied from the multiplexer 54, and supplies the resulting LDPC code to the LDPC decoder 166.

In step S113, the LDPC decoder 166 performs LDPC decoding on the LDPC code supplied from the column twist deinterleaver 55 by using the parity check matrix H that the LDPC encoder 115 illustrated in FIG. 8 has used for LDPC encoding, that is, by using a transformed parity check matrix obtained by performing at least column permutation corresponding to parity interleaving on the parity check matrix H, and outputs the resulting data to the BCH decoder 167 as a result of decoding the LDPC target data.

Note that, also in FIG. 117, similarly to the case illustrated in FIG. 9, the multiplexer 54 that performs inverse permutation processing and the column twist deinterleaver 55 that performs column twist deinterleaving are configured as separate units, for convenience of illustration. However, the multiplexer 54 and the column twist deinterleaver 55 may be integrated into a single unit.

In addition, if the bit interleaver 116 illustrated in FIG. 9 does not perform column twist interleaving, the bit deinterleaver 165 illustrated in FIG. 117 need not be provided with the column twist deinterleaver 55.

Next, LDPC decoding performed by the LDPC decoder 166 illustrated in FIG. 116 will be described in further detail.

As described above, the LDPC decoder 166 illustrated in FIG. 116 performs LDPC decoding on the LDPC code supplied from the column twist deinterleaver 55, on which inverse permutation processing and column twist deinterleaving have been performed but parity deinterleaving has not been performed, by using a transformed parity check matrix obtained by performing at least column permutation corresponding to parity interleaving on the parity check matrix H that the LDPC encoder 115 illustrated in FIG. 8 has used for LDPC encoding.

Here, LDPC decoding may be performed using a transformed parity check matrix so as to keep the operating frequency within a sufficiently feasible range while reducing the size of circuitry. Such LDPC decoding has been previously proposed (see, for example, Japanese Patent No. 4224777).

Accordingly, first, LDPC decoding using a transformed parity check matrix, which has been previously proposed, will be described with reference to FIGS. 119 to 122.

FIG. 119 illustrates an example of a parity check matrix H of an LDPC code having a code length N of 90 and a code rate of 2/3.

Note that, in FIG. 119 (also in FIGS. 120 and 121, described below), “0” is represented by a period (“.”).

In the parity check matrix H illustrated in FIG. 119, a parity matrix has a stepwise structure.

FIG. 120 illustrates a parity check matrix H′ obtained by performing row permutation of Expression (11) and column permutation of Expression (12) on the parity check matrix H illustrated in FIG. 119.

Row permutation:(6s+t+1)-th row→(5t+s+1)-th row   (11)

Column permutation:(6x+y+61)-th column→(5y+x+61)-th column   (12)

Note that, in Expressions (11) and (12), s, t, x, and y are integers in the ranges of 0≤s<5, 0≤t<6, 0≤x<5, and 0≤t<6, respectively.

The row permutation of Expression (11) allows permutation such that the 1st, 7th, 13th, 19th, and 25th rows, whose numbers are divided by 6 yielding a remainder of 1, are replaced with the 1st, 2nd, 3rd, 4th, and 5th rows, respectively, and the 2nd, 8th, 14th, 20th, and 26th rows, whose numbers are divided by 6 yielding a remainder of 2, are replaced with the 6th, 7th, 8th, 9th, and 10th rows, respectively.

Further, the column permutation of Expression (12) allows permutation such that the 61st, 67th, 73rd, 79th, and 85th columns, whose numbers are divided by 6 yielding a remainder of 1, among the columns subsequent to the 61st column (parity matrix), are replaced with the 61st, 62nd, 63rd, 64th, and 65th columns, respectively, and the 62nd, 68th, 74th, 80th, and 86th columns, whose numbers are divided by 6 yielding a remainder of 2, are replaced with the 66th, 67th, 68th, 69th, and 70th columns, respectively.

A matrix obtained by performing row and column permutations on the parity check matrix H illustrated in FIG. 119 in the way described above is the parity check matrix H′ illustrated in FIG. 120.

Here, the row permutation of the parity check matrix H would not affect the order of the code bits of the LDPC code.

Furthermore, the column permutation of Expression (12) corresponds to parity interleaving that is performed to interleave the (K+qx+y+1)-th code bit to the (K+Py+x+1)-th code bit position as described above, when the information length K is 60, the number of unit columns P of the cyclic structure is 5, and the divisor q (=M/P) of the parity length M (in the illustrated example, 30) is 6.

Accordingly, the parity check matrix H′ illustrated in FIG. 120 is a transformed parity check matrix obtained by performing at least column permutation to replace the (K+qx+y+1)-th column of the parity check matrix (hereinafter referred to as an “original parity check matrix” as appropriate) H illustrated in FIG. 119 with the (K+Py+x+1)-th column.

Multiplying the transformed parity check matrix H′ illustrated in FIG. 120 by an LDPC code obtained by performing the same permutation as that of Expression (12) on the LDPC code of the original parity check matrix H illustrated in FIG. 119 yields a zero vector. More specifically, if a row vector obtained by performing column permutation of Expression (12) on a row vector c as an LDPC code (i.e., a code word) of the original parity check matrix H is represented by c′, Hc^(T) is a zero vector due to the nature of the parity check matrix, and therefore H′c′^(T) is also a zero vector.

Thus, the transformed parity check matrix H′ illustrated in FIG. 120 is a parity check matrix of an LDPC code c′ obtained by performing column permutation of Expression (12) on the LDPC code c of the original parity check matrix H.

Accordingly, a similar result of decoding to that obtained by decoding the LDPC code of the original parity check matrix H using the parity check matrix H may be obtained by decoding (LDPC decoding) the LDPC code c′, which is obtained by performing column permutation of Expression (12) on the LDPC code c of the original parity check matrix H, using the transformed parity check matrix H′ illustrated in FIG. 120 and then performing the inverse of the column permutation of Expression (12) on the decoded LDPC code c′.

FIG. 121 illustrates the transformed parity check matrix H′ illustrated in FIG. 120 whose elements are spaced apart from one another in units of 5×5 matrices.

In FIG. 121, the transformed parity check matrix H′ is represented by a combination of 5×5 (=P×P) unit matrices, matrices each having one or more elements of 1 in a unit matrix which are replaced by elements of 0 (hereinafter referred to as “quasi-unit matrices” as appropriate), matrices produced by cyclically shifting a unit matrix or a quasi-unit matrix (hereinafter referred to as “shift matrices” as appropriate), matrices each of which is the sum of two or more of a unit matrix, a quasi-unit matrix, and a shift matrix (hereinafter referred to as “sum matrices” as appropriate), and 5×5 zero matrices.

The transformed parity check matrix H′ illustrated in FIG. 121 can be said to be composed of 5×5 unit matrices, quasi-unit matrices, shift matrices, sum matrices, and zero matrices. These 5×5 matrices (unit matrices, quasi-unit matrices, shift matrices, sum matrices, and zero matrices) constituting the transformed parity check matrix H′ are hereinafter referred to as “component matrices” as appropriate.

An LDPC code of a parity check matrix represented by P×P component matrices may be decoded using an architecture that simultaneously performs check node computation and variable node computation each for P nodes.

FIG. 122 is a block diagram illustrating an example configuration of a decoding device that performs the decoding operation described above.

More specifically, FIG. 122 illustrates an example configuration of a decoding device configured to decode an LDPC code by using the transformed parity check matrix H′ illustrated in FIG. 121, which is obtained by performing at least column permutation of Expression (12) on the original parity check matrix H illustrated in FIG. 119.

The decoding device illustrated in FIG. 122 includes an edge data storage memory 300 having six FIFOs 300 ₁ to 300 ₆, a selector 301 for selecting one of the FIFOs 300 ₁ to 300 ₆, a check node calculation unit 302, two cyclic shift circuits 303 and 308, an edge data storage memory 304 having 18 FIFOs 304 ₁ to 304 ₁₈, a selector 305 for selecting one of the FIFOs 304 ₁ to 304 ₁₈, a received data memory 306 for storing received data, a variable node calculation unit 307, a decoded word calculation unit 309, a received data reordering unit 310, and a decoded data reordering unit 311.

First, a description will be made of a method for storing data in the edge data storage memories 300 and 304.

The edge data storage memory 300 includes the six FIFOs 300 ₁ to 300 ₆, the number of which is equal to a value obtained by dividing the number of rows of the transformed parity check matrix H′ illustrated in FIG. 121, i.e., 30, by the number of rows of each component matrix (i.e., the number of unit columns P of the cyclic structure), i.e., 5. Each of the FIFOs 300 _(y) (y=1, 2, . . . , 6) includes storage areas of multiple stages, and is configured such that messages corresponding to five edges, the number of which is equal to the number of rows and the number of columns of each component matrix (i.e., the number of unit columns P of the cyclic structure), can be simultaneously read from and written to the storage area of each stage. In addition, the number of stages of the storage areas of each of the FIFOs 300 _(y) is 9, which is the maximum of the numbers of is (Hamming weights) in the row direction of the transformed parity check matrix illustrated in FIG. 121.

Data (i.e., messages v₁ from variable nodes) corresponding to the positions of is in the first to fifth rows of the transformed parity check matrix H′ illustrated in FIG. 121 is stored in the FIFO 300 ₁ in such a manner that every row is filled with the data elements in the lateral direction (i.e., 0s are ignored). More specifically, if the element in the j-th row and the i-th column is represented by (j,i), data corresponding to the positions of is in the 5×5 unit matrix of (1,1) to (5,5) of the transformed parity check matrix H′ is stored in the storage area of the first stage of the FIFO 300 ₁. Data corresponding to the positions of is in the shift matrix (which is a shift matrix obtained by cyclically shifting the 5×5 unit matrix to the right by three elements) of (1,21) to (5,25) of the transformed parity check matrix H′ is stored in the storage area of the second stage. Similarly, data is stored in the storage areas of the third to eighth stages in association with the transformed parity check matrix H′. Furthermore, data corresponding to the positions of is in the shift matrix (which is a shift matrix obtained by replacing is in the first row with 0s in the 5×5 unit matrix and cyclically shifting the 5×5 unit matrix to the left by one element) of (1,86) to (5,90) of the transformed parity check matrix H′ is stored in the storage area of the ninth stage.

Data corresponding to the positions of is in the sixth to tenth rows of the transformed parity check matrix H′ illustrated in FIG. 121 is stored in the FIFO 300 ₂. More specifically, data corresponding to the positions of is in a first shift matrix included in a sum matrix (which is a sum matrix representing the sum of a first shift matrix obtained by cyclically shifting the 5×5 unit matrix to the right by one element and a second shift matrix obtained by cyclically shifting the 5×5 unit matrix to the right by two elements) of (6,1) to (10,5) of the transformed parity check matrix H′ is stored in the storage area of the first stage of the FIFO 300 ₂. Furthermore, data corresponding to the positions of is in the second shift matrix included in the sum matrix of (6,1) to (10,5) of the transformed parity check matrix H′ is stored in the storage area of the second stage.

More specifically, in the case of a component matrix having a weight of 2 or more, when the component matrix is represented by the sum of two or more of a P×P unit matrix having a weight of 1, a quasi-unit matrix produced by replacing one or more elements of 1 in the unit matrix with elements of 0, and a shift matrix produced by cyclically shifting the unit matrix or the quasi-unit matrix, data corresponding to the positions of is in the unit matrix having a weight of 1, the quasi-unit matrix, or the shift matrix (i.e., messages corresponding to edges belonging to the unit matrix, the quasi-unit matrix, or the shift matrix) is stored in the same address (i.e., the same FIFO among the FIFOs 300 ₁ to 300 ₆).

Data is also stored in the storage areas of the subsequent third to ninth stages in association with the transformed parity check matrix H′.

Similarly, data is stored in the FIFOs 300 ₃ to 300 ₆ in association with the transformed parity check matrix H′.

The edge data storage memory 304 includes 18 FIFOs 304 ₁ to 304 ₁₈, the number of which is equal to a value obtained by dividing the number of columns of the transformed parity check matrix H′, i.e., 90, by the number of columns of each component matrix (i.e., the number of unit columns P of the cyclic structure), i.e., 5. Each of the FIFOs 304 _(x) (x=1, 2, . . . , 18) includes storage areas of multiple stages, and is configured such that messages corresponding to five edges, the number of which is equal to the number of rows and the number of columns of each component matrix (i.e., the number of unit columns P of the cyclic structure), can be simultaneously read from and written to the storage area of each stage.

Data (i.e., messages u_(j) from check nodes) corresponding to the positions of is in the first to fifth columns of the transformed parity check matrix H′ illustrated in FIG. 121 is stored in the FIFO 304 ₁ in such a manner that every column is filled with the data elements in the longitudinal direction (i.e., 0s are ignored). Specifically, data corresponding to the positions of is in the 5×5 unit matrix of (1,1) to (5,5) of the transformed parity check matrix H′ is stored in the storage area of the first stage of the FIFO 304 ₁. Data corresponding to the positions of is in a first shift matrix included in a sum matrix (which is a sum matrix representing the sum of a first shift matrix obtained by cyclically shifting the 5×5 unit matrix to the right by one element and a second shift matrix obtained by cyclically shifting the 5×5 unit matrix to the right by two elements) of (6,1) to (10,5) of the transformed parity check matrix H′ is stored in the storage area of the second stage. Furthermore, data corresponding to the positions of is in the second shift matrix included in the sum matrix of (6,1) to (10,5) of the transformed parity check matrix H′ is stored in the storage area of the third stage.

More specifically, in the case of a component matrix having a weight of 2 or more, when the component matrix is represented by the sum of two or more of a P×P unit matrix having a weight of 1, a quasi-unit matrix produced by replacing one or more elements of 1 in the unit matrix with elements of 0, and a shift matrix produced by cyclically shifting the unit matrix or the quasi-unit matrix, data corresponding to the positions of is in the unit matrix having a weight of 1, the quasi-unit matrix, or the shift matrix (i.e., messages corresponding to edges belonging to the unit matrix, the quasi-unit matrix, or the shift matrix) is stored in the same address (i.e., the same FIFO among the FIFOs 304 ₁ to 304 ₁₈).

Data is also stored in the storage areas of the subsequent fourth and fifth stages in association with the transformed parity check matrix H′. The number of stages of storage areas of the FIFO 304 ₁ is 5, which is the maximum of the numbers of is (Hamming weights) in the row direction in the first to fifth columns of the transformed parity check matrix H′.

Similarly, data is also stored in the FIFOs 304 ₂ and 304 ₃ in association with the transformed parity check matrix H′, with the respective lengths (the numbers of stages) being 5. Data is also stored in the FIFOs 304 ₄ to 304 ₁₂ in association with the transformed parity check matrix H′, with the respective lengths being 3. Data is also stored in the FIFOs 304 ₁₃ to 304 ₁₈ in association with the transformed parity check matrix H′, with the respective lengths being 2.

A description will now be made of the operation of the decoding device illustrated in FIG. 122.

The edge data storage memory 300, which includes the six FIFOs 300 ₁ to 300 ₆, selects a FIFO to store data from among the FIFOs 300 ₁ to 300 ₆ in accordance with information (matrix data) D312 indicating which row in the transformed parity check matrix H′ illustrated in FIG. 121 five messages D311 supplied from the cyclic shift circuit 308 located upstream of the edge data storage memory 300 belong to, and collectively stores the five messages D311 in the selected FIFO in order. Further, when reading data, the edge data storage memory 300 reads five messages D300 ₁ in order from the FIFO 300 ₁, and supplies the read messages D300 ₁ to the selector 301 located downstream of the edge data storage memory 300. After the reading of messages from the FIFO 300 ₁ is completed, the edge data storage memory 300 also reads messages in order from the FIFOs 300 ₂ to 300 ₆, and supplies the read messages to the selector 301.

The selector 301 selects five messages received from a FIFO from which data is currently being read among the FIFOs 300 ₁ to 300 ₆ in accordance with a selection signal D301, and supplies the selected messages as messages D302 to the check node calculation unit 302.

The check node calculation unit 302 includes five check node calculators 302 ₁ to 302 ₅, and performs check node computation in accordance with Expression (7) using the messages D302 (D302 ₁ to D302 ₅) (corresponding to messages v₁ in Expression (7)) supplied through the selector 301. The check node calculation unit 302 supplies five messages D303 (D303 ₁ to D303 ₅) (corresponding to messages u_(j) in Expression (7)) obtained as a result of the check node computation to the cyclic shift circuit 303.

The cyclic shift circuit 303 cyclically shifts the five messages D303 ₁ to D303 ₅ determined by the check node calculation unit 302 on the basis of information (matrix data) D305 indicating the number of original unit matrices (or quasi-unit matrices) which have been cyclically shifted in the transformed parity check matrix H′ to obtain the corresponding edge, and supplies results to the edge data storage memory 304 as messages D304.

The edge data storage memory 304, which includes the 18 FIFOs 304 ₁ to 304 ₁₈, selects an FIFO to store data from among the FIFOs 304 ₁ to 304 ₁₈ in accordance with information D305 indicating which row in the transformed parity check matrix H′ the five messages D304 supplied from the cyclic shift circuit 303 located upstream of the edge data storage memory 304 belong to, and collectively stores the five messages D304 in the selected FIFO in order. Further, when reading data, the edge data storage memory 304 reads five messages D306 ₁ in order from the FIFO 304 ₁, and supplies the read messages D306 ₁ to the selector 305 located downstream of the edge data storage memory 304. After the reading of data from the FIFO 304 ₁ is completed, the edge data storage memory 304 also reads messages in order from the FIFOs 304 ₂ to 304 ₁₈, and supplies the read messages to the selector 305.

The selector 305 selects five messages from a FIFO from which data is currently being read among the FIFOs 304 ₁ to 304 ₁₈ in accordance with a selection signal D307, and supplies the selected messages as messages D308 to the variable node calculation unit 307 and the decoded word calculation unit 309.

On the other hand, the received data reordering unit 310 reorders an LDPC code D313 corresponding to the parity check matrix H illustrated in FIG. 119, which has been received through the communication path 13, by performing column permutation of Expression (12), and supplies the resulting data as received data D314 to the received data memory 306. The received data memory 306 calculates reception LLRs (log-likelihood ratios) from the received data D314 supplied from the received data reordering unit 310, and stores the reception LLRs. The received data reordering unit 310 further collectively supplies the reception LLRs in units of five reception LLRs as reception values D309 to the variable node calculation unit 307 and the decoded word calculation unit 309.

The variable node calculation unit 307 includes five variable node calculators 307 ₁ to 307 ₅, and performs variable node computation in accordance with Expression (1) using the messages D308 (D308 ₁ to D308 ₅) (i.e., messages u_(j) in Expression (1)) supplied through the selector 305 and the five reception values D309 (reception values u_(0i) in Expression (1)) supplied from the received data memory 306. The variable node calculation unit 307 supplies messages D310 (D310 ₁ to D310 ₅) (i.e., messages v_(i) in Expression (1)) obtained as a result of the computation to the cyclic shift circuit 308.

The cyclic shift circuit 308 cyclically shifts the messages D310 ₁ to D310 ₅ calculated by the variable node calculation unit 307 on the basis of information indicating the number of original unit matrices (or quasi-unit matrices) which have been cyclically shifted in the transformed parity check matrix H′ to obtain the corresponding edge, and supplies results to the edge data storage memory 300 as messages D311.

The series of operations described above can be performed once to perform single decoding of an LDPC code (variable node computation and check node computation). After decoding an LDPC code a certain number of times, the decoding device illustrated in FIG. 122 determines and outputs final decoded data through the decoded word calculation unit 309 and the decoded data reordering unit 311.

More specifically, the decoded word calculation unit 309 includes five decoded word calculators 309 ₁ to 309 ₅, and serves as a final stage of a plurality of decoding operations to calculate decoded data (i.e., a decoded word) in accordance with Expression (5) using the five messages D308 (D308 ₁ to D308 ₅) (i.e., messages u_(j) in Expression (5)) output from the selector 305 and the five reception values D309 (i.e., reception values u_(0i) in Expression (5)) supplied from the received data memory 306. The decoded word calculation unit 309 supplies decoded data D315 obtained as a result of the calculation to the decoded data reordering unit 311.

The decoded data reordering unit 311 changes the order of the decoded data D315 supplied from the decoded word calculation unit 309 by performing the inverse of the column permutation of Expression (12), and outputs the resulting data as final decoded data D316.

As described above, one or both of the row permutation and the column permutation are performed on the parity check matrix (i.e., the original parity check matrix) to convert the parity check matrix into a parity check matrix (i.e., a transformed parity check matrix) that can be represented by a combination of component matrices, namely, a P×P unit matrix, a quasi-unit matrix produced by replacing one or more elements of 1 with elements of 0, a shift matrix produced by cyclically shifting the unit matrix or the quasi-unit matrix, a sum matrix representing the sum of two or more of the unit matrix, the quasi-unit matrix, and the shift matrix, and a P×P zero matrix. This allows decoding of an LDPC code by using an architecture that simultaneously performs check node computation and variable node computation each for P nodes, where P is less than the number of rows or the number of columns of the parity check matrix. The use of an architecture that simultaneously performs node computation (computation of check nodes and computation of variable nodes) for P nodes, where P is less than the number of rows or the number of columns of a parity check matrix, makes it possible to perform multiple repetitive decoding while keeping the operating frequency within a feasible range, compared to the case where node computation is simultaneously performed for nodes, the number of which is equal to the number of rows or the number of columns of a parity check matrix.

Similarly to the decoding device illustrated in FIG. 122, the LDPC decoder 166 included in the receiving device 12 illustrated in FIG. 116 is configured to perform LDPC decoding by, for example, simultaneously performing check node computation and variable node computation each for P nodes.

More specifically, it is assumed now that, for ease of description, the parity check matrix of the LDPC code output from the LDPC encoder 115 included in the transmitting device 11 illustrated in FIG. 8 is, for example, the parity check matrix H illustrated in FIG. 119 in which a parity matrix has a stepwise structure. In this case, the parity interleaver 23 of the transmitting device 11 performs parity interleaving to interleave the (K+qx+y+1)-th code bit to the (K+Py+x+1)-th code bit position with the information length K being 60, the number of unit columns P of the cyclic structure being 5, and the divisor q (=M/P) of the parity length M being 6.

As described above, this parity interleaving operation corresponds to the column permutation of Expression (12). Thus, it is not necessary for the LDPC decoder 166 to perform the column permutation of Expression (12).

In the receiving device 12 illustrated in FIG. 116, therefore, as described above, an LDPC code on which parity deinterleaving has not been performed, that is, an LDPC code on which the column permutation of Expression (12) has been performed, is supplied from the column twist deinterleaver 55 to the LDPC decoder 166. The LDPC decoder 166 performs processing similar to that of the decoding device illustrated in FIG. 122, except that the column permutation of Expression (12) is not performed.

More specifically, FIG. 123 illustrates an example configuration of the LDPC decoder 166 illustrated in FIG. 116.

In FIG. 123, the LDPC decoder 166 has a configuration similar to the decoding device illustrated in FIG. 122, except that the received data reordering unit 310 illustrated in FIG. 122 is not included, and performs processing similar to that of the decoding device illustrated in FIG. 122, except that the column permutation of Expression (12) is not performed, which is not described herein.

As described above, the LDPC decoder 166 may be configured without including the received data reordering unit 310, and can be smaller in size than the decoding device illustrated in FIG. 122.

Note that, in FIGS. 119 to 123, for ease of illustration, the code length N of an LDPC code is 90, the information length K is 60, the number of unit columns P of the cyclic structure (i.e., the number of rows and the number of columns of a component matrix) is 5, and the divisor q (=M/P) of the parity length M is 6. However, the code length N, the information length K, the number of unit columns P of the cyclic structure, and the divisor q (=M/P) are not limited to the values described above.

More specifically, the LDPC encoder 115 in the transmitting device 11 illustrated in FIG. 8 outputs an LDPC code with, for example, the code length N being 64800, 16200, or the like, the information length K being given by N−Pq (=N−M), the number of unit columns P of the cyclic structure being 360, and the divisor q being given by M/P. The LDPC decoder 166 illustrated in FIG. 123 may be used to perform LDPC decoding on the LDPC code described above by simultaneously performing check node computation and variable node computation each for P nodes.

FIG. 124 includes diagrams depicting the processing of the multiplexer 54 included in the bit deinterleaver 165 illustrated in FIG. 117.

More specifically, part A of FIG. 124 illustrates an example functional configuration of the multiplexer 54.

The multiplexer 54 includes an inverse permutation unit 1001 and a memory 1002.

The multiplexer 54 performs inverse permutation processing (which is the inverse of permutation processing), corresponding to the permutation processing performed by the demultiplexer 25 of the transmitting device 11, on the symbol bits of the symbols supplied from the QAM decoder 164 located upstream of the multiplexer 54. That is, the multiplexer 54 performs inverse permutation processing to restore the positions of the code bits (symbol bits) of the LDPC code that have been permuted through the permutation processing to the original positions, and supplies the resulting LDPC code to the column twist deinterleaver 55 located downstream of the multiplexer 54.

More specifically, mb symbol bits y₀, y₁, . . . , y_(mb-1) of b symbols are supplied to the inverse permutation unit 1001 in the multiplexer 54 in units of (consecutive) b symbols.

The inverse permutation unit 1001 performs inverse permutation to restore the mb symbol bits y₀ to y_(mb-1) to the order of the mb original code bits b₀, b₁, . . . , b_(mb-1) (i.e., the order of the code bits b₀ to b_(mb-1) before the permutation unit 32 included in the demultiplexer 25 on the transmitting device 11 side performs permutation), and outputs the resulting mb code bits b₀ to b_(mb-1).

Similarly to the memory 31 included in the demultiplexer 25 on the transmitting device 11 side, the memory 1002 has a storage capacity to store mb bits in its row (horizontal) direction and N/(mb) bits in its column (vertical) direction. In other words, the memory 1002 includes mb columns for storing N/(mb) bits.

Note that code bits of the LDPC code output from the inverse permutation unit 1001 are written to the memory 1002 in the direction in which a code bit is read from the memory 31 in the demultiplexer 25 of the transmitting device 11, and the code bits written in the memory 1002 are read from the memory 1002 in the direction in which a code bit is written to the memory 31.

Accordingly, as illustrated in part A of FIG. 124, the multiplexer 54 of the receiving device 12 writes code bits of the LDPC code output from the inverse permutation unit 1001 in the row direction in units of mb bits, where the writing operation moves from the top to the bottom of the memory 1002, starting from the first row.

Further, when the writing of code bits corresponding to one code length is completed, the multiplexer 54 reads the code bits from the memory 1002 in the column direction, and supplies the read code bits to the column twist deinterleaver 55 located downstream of the multiplexer 54.

Here, part B of FIG. 124 is a diagram illustrating the reading of code bits from the memory 1002.

The multiplexer 54 reads code bits of the LDPC code (in the column direction) from the top to the bottom of each of the columns of the memory 1002, where the reading operation moves toward the right, starting from the leftmost column.

FIG. 125 is a diagram depicting the processing of the column twist deinterleaver 55 included in the bit deinterleaver 165 illustrated in FIG. 117.

More specifically, FIG. 125 illustrates an example configuration of the memory 1002 of the multiplexer 54.

The memory 1002 has a storage capacity to store mb bits in its column (vertical) direction and N/(mb) bits in its row (horizontal) direction, and includes mb columns.

The column twist deinterleaver 55 performs column twist deinterleaving by controlling a read start position when code bits of the LDPC code are written to the memory 1002 in the row direction and are read from the memory 1002 in the column direction.

More specifically, the column twist deinterleaver 55 performs inverse reordering processing to restore the code bits whose order has been changed through column twist interleaving to the original order, by changing the read start position with which the reading of a code bit is started, as desired, for each of a plurality of columns.

Here, FIG. 125 illustrates an example configuration of the memory 1002 in a case where, as described with reference to FIG. 28, the modulation scheme is 16APSK, 16QAM, or the like and the multiple b is 1. In this case, the number of bits m of one symbol is 4, and the memory 1002 includes 4 (=mb) columns.

Instead of the multiplexer 54, the column twist deinterleaver 55 writes code bits of the LDPC code output from the inverse permutation unit 1001 in the row direction, where the writing operation moves downward sequentially from the first row of the memory 1002.

Further, when the writing of code bits corresponding to one code length is completed, the column twist deinterleaver 55 reads the code bits from the memory 1002 (in the column direction) from the top to the bottom, where the reading operation moves toward the right, starting from the leftmost column.

Note that the column twist deinterleaver 55 reads code bits from the memory 1002, using, as a read start position of the code bit, the write start position from which the column twist interleaver 24 on the transmitting device 11 side writes a code bit.

More specifically, if the address of the position of the first (or top) of each column is represented by 0 and the addresses of the respective positions in the column direction are represented by integers arranged in ascending order, the column twist deinterleaver 55 sets the read start position for the leftmost column to the position at the address 0, the read start position for the second column (from the left) to the position at the address 2, the read start position for the third column to the position at the address 4, and the read start position for the fourth column to the position at the address 7 in a case where the modulation scheme is 16APSK or 16QAM and the multiple b is 1.

Note that, after reading code bits up to the bottom of the column for which the read start position is set to a position other than the position at the address 0, the column twist deinterleaver 55 returns to the first position (i.e., the position at the address 0), and reads code bits up to the position immediately before the read start position. The column twist deinterleaver 55 then performs reading from the subsequent (right) column.

The column twist deinterleaving operation described above allows the order of code bits that have been reordered through column twist interleaving to return to the original order.

FIG. 126 is a block diagram illustrating another example configuration of the bit deinterleaver 165 illustrated in FIG. 116.

Note that, in FIG. 126, portions corresponding to those illustrated in FIG. 117 are assigned the same reference numerals, and a description thereof will be omitted hereinafter, as appropriate.

More specifically, the bit deinterleaver 165 illustrated in FIG. 126 has a configuration similar to that illustrated in FIG. 117, except that a parity deinterleaver 1011 is further included.

In FIG. 126, the bit deinterleaver 165 includes a multiplexer (MUX) 54, a column twist deinterleaver 55, and a parity deinterleaver 1011, and performs bit deinterleaving on code bits of the LDPC code supplied from the QAM decoder 164.

More specifically, the multiplexer 54 performs inverse permutation processing (which is the inverse of permutation processing), corresponding to the permutation processing performed by the demultiplexer 25 of the transmitting device 11, on the LDPC code supplied from the QAM decoder 164. That is, the multiplexer 54 performs inverse permutation processing to restore the positions of the code bits permuted through permutation processing to the original positions, and supplies the resulting LDPC code to the column twist deinterleaver 55.

The column twist deinterleaver 55 performs column twist deinterleaving, corresponding to column twist interleaving as the reordering processing performed by the column twist interleaver 24 of the transmitting device 11, on the LDPC code supplied from the multiplexer 54.

The LDPC code obtained as a result of column twist deinterleaving is supplied from the column twist deinterleaver 55 to the parity deinterleaver 1011.

The parity deinterleaver 1011 performs parity deinterleaving (which is the inverse of parity interleaving operation), corresponding to parity interleaving performed by the parity interleaver 23 of the transmitting device 11, on the code bits on which column twist deinterleaving has been performed by the column twist deinterleaver 55. That is, the parity deinterleaver 1011 performs parity deinterleaving to restore the code bits of the LDPC code whose order has been changed through parity interleaving to the original order.

The LDPC code obtained as a result of parity deinterleaving is supplied from the parity deinterleaver 1011 to the LDPC decoder 166.

Accordingly, the bit deinterleaver 165 illustrated in FIG. 126 supplies an LDPC code on which inverse permutation processing, column twist deinterleaving, and parity deinterleaving have been performed, i.e., an LDPC code obtained through LDPC encoding in accordance with the parity check matrix H, to the LDPC decoder 166.

The LDPC decoder 166 performs LDPC decoding on the LDPC code supplied from the bit deinterleaver 165 by using the parity check matrix H that the LDPC encoder 115 of the transmitting device 11 has used for LDPC encoding. More specifically, the LDPC decoder 166 performs LDPC decoding on the LDPC code supplied from the bit deinterleaver 165 by using the parity check matrix H that the LDPC encoder 115 of the transmitting device 11 has used for LDPC encoding, or by using a transformed parity check matrix obtained by performing at least column permutation, corresponding to parity interleaving, on the parity check matrix H.

Here, in FIG. 126, an LDPC code obtained through LDPC encoding in accordance with the parity check matrix H is supplied from (the parity deinterleaver 1011 of) the bit deinterleaver 165 to the LDPC decoder 166. Accordingly, in a case where the LDPC decoding of the LDPC code is performed using the parity check matrix H that the LDPC encoder 115 of the transmitting device 11 has used for LDPC encoding, the LDPC decoder 166 may be implemented as, for example, a decoding device configured to perform LDPC decoding using a full serial decoding method for sequentially performing computation of messages (i.e., check node messages and variable node messages) on a node-by-node basis, or a decoding device configured to perform LDPC decoding using a full parallel decoding method for simultaneously (or in parallel) performing computation of messages for all the nodes.

Furthermore, in a case where the LDPC decoder 166 performs LDPC decoding on an LDPC code using a transformed parity check matrix obtained by performing at least column permutation, corresponding to parity interleaving, on the parity check matrix H that the LDPC encoder 115 of the transmitting device 11 has used for LDPC encoding, the LDPC decoder 166 may be implemented as a decoding device having an architecture that simultaneously performs check node computation and variable node computation each for P (or a divisor of P other than 1) nodes, which is the decoding device (FIG. 122) including the received data reordering unit 310 configured to perform column permutation similar to column permutation for obtaining a transformed parity check matrix on an LDPC code to reorder the code bits of the LDPC code.

Note that, in FIG. 126, the multiplexer 54 that performs inverse permutation processing, the column twist deinterleaver 55 that performs column twist deinterleaving, and the parity deinterleaver 1011 that performs parity deinterleaving are configured as separate units, for convenience of illustration. However, two or more of the multiplexer 54, the column twist deinterleaver 55, and the parity deinterleaver 1011 may be integrated into a single unit, similarly to the parity interleaver 23, the column twist interleaver 24, and the demultiplexer 25 of the transmitting device 11.

In addition, if the bit interleaver 116 (FIG. 8) of the transmitting device 11 is configured without including the parity interleaver 23 or the column twist interleaver 24, the bit deinterleaver 165 illustrated in FIG. 126 may be configured without including the column twist deinterleaver 55 or the parity deinterleaver 1011.

Also in this case, the LDPC decoder 166 may be implemented as a decoding device of the full serial decoding type that performs LDPC decoding using the parity check matrix H itself, a decoding device of the full parallel decoding type that performs LDPC decoding using the parity check matrix H itself, or the decoding device (FIG. 122) including the received data reordering unit 310 configured to perform LDPC decoding by simultaneously performing check node computation and variable node computation each for P nodes using a transformed parity check matrix H′.

[Example Configuration of Receiving System]

FIG. 127 is a block diagram illustrating a first example configuration of a receiving system to which the receiving device 12 is applicable.

In FIG. 127, the receiving system includes an acquisition unit 1101, a transmission path decoding processing unit 1102, and an information source decoding processing unit 1103.

The acquisition unit 1101 acquires a signal including an LDPC code obtained by performing at least LDPC encoding on LDPC target data such as image data and audio data of a program via a transmission path (or communication path) (not illustrated) such as terrestrial digital broadcasting, satellite digital broadcasting, a CATV network, the Internet, or any other suitable network, and supplies the signal to the transmission path decoding processing unit 1102.

Here, in a case where the acquisition unit 1101 acquires a signal broadcasted from, for example, a broadcast station via terrestrial, satellite, CATV (Cable Television), or any other network, the acquisition unit 1101 may be implemented as a tuner, an STB (Set Top Box), or the like. Further, in a case where the acquisition unit 1101 acquires a signal transmitted using, for example, multicast technology like IPTV (Internet Protocol Television) from a web server, the acquisition unit 1101 may be implemented as a network I/F (Interface) such as a NIC (Network Interface Card).

The transmission path decoding processing unit 1102 corresponds to the receiving device 12. The transmission path decoding processing unit 1102 performs a transmission path decoding process, including at least processing for correcting errors caused in a transmission path, on the signal acquired by the acquisition unit 1101 via a transmission path, and supplies the resulting signal to the information source decoding processing unit 1103.

More specifically, the signal acquired by the acquisition unit 1101 via a transmission path is a signal obtained by performing at least error correcting encoding to correct errors caused in a transmission path. The transmission path decoding processing unit 1102 performs a transmission path decoding process such as an error correction process on the above-described signal.

Here, examples of the error correcting encoding include LDPC encoding and BCH encoding. Here, at least LDPC encoding is performed as error correcting encoding.

Furthermore, the transmission path decoding process may include, for example, demodulation of modulation signals.

The information source decoding processing unit 1103 performs an information source decoding process, including at least processing for expanding compressed information into original information, on the signal on which the transmission path decoding process has been performed.

More specifically, the signal acquired by the acquisition unit 1101 via a transmission path may have been subjected to compression encoding for compressing information in order to reduce the amount of data such as image data and audio data as information. In this case, the information source decoding processing unit 1103 performs an information source decoding process, such as processing for expanding compressed information into original information (i.e., expansion processing), on the signal on which the transmission path decoding process has been performed.

Note that, if the signal acquired by the acquisition unit 1101 via a transmission path has not been subjected to compression encoding, the information source decoding processing unit 1103 does not perform processing for expanding compressed information into original information.

Here, examples of the expansion processing include MPEG decoding. Furthermore, the transmission path decoding process may include descrambling and so forth in addition to expansion processing.

In the receiving system having the configuration described above, the acquisition unit 1101 acquires a signal obtained by performing compression encoding such as MPEG encoding and error correcting encoding such as LDPC encoding on data such as image data and audio data, via a transmission path, and supplies the acquired signal to the transmission path decoding processing unit 1102.

The transmission path decoding processing unit 1102 performs a transmission path decoding process, for example, processing similar to that performed by the receiving device 12, on the signal supplied from the acquisition unit 1101, and supplies the resulting signal to the information source decoding processing unit 1103.

The information source decoding processing unit 1103 performs an information source decoding process such as MPEG decoding on the signal supplied from the transmission path decoding processing unit 1102, and outputs the resulting images or audio.

The receiving system illustrated in FIG. 127 as described above may be applied to, for example, a television tuner or the like that receives television broadcasting as digital broadcasting.

Note that the acquisition unit 1101, the transmission path decoding processing unit 1102, and the information source decoding processing unit 1103 may be constructed as single independent devices (hardware (such as ICs (Integrated Circuits)) or software modules).

In addition, the acquisition unit 1101, the transmission path decoding processing unit 1102, and the information source decoding processing unit 1103 may be configured such that the combination of the acquisition unit 1101 and the transmission path decoding processing unit 1102, the combination of the transmission path decoding processing unit 1102 and the information source decoding processing unit 1103, or the combination of the acquisition unit 1101, the transmission path decoding processing unit 1102, and the information source decoding processing unit 1103 is constructed as a single independent device.

FIG. 128 is a block diagram illustrating a second example configuration of the receiving system to which the receiving device 12 is applicable.

Note that, in FIG. 128, portions corresponding to those illustrated in FIG. 127 are assigned the same reference numerals, and a description thereof will be omitted hereinafter, as appropriate.

The receiving system illustrated in FIG. 128 is common to that illustrated in FIG. 127 in that the acquisition unit 1101, the transmission path decoding processing unit 1102, and the information source decoding processing unit 1103 are included, and is different from that illustrated in FIG. 127 in that an output unit 1111 is further included.

The output unit 1111 may be, for example, a display device configured to display an image or a speaker configured to output audio, and outputs images, audio, or the like as signals output from the information source decoding processing unit 1103. In other words, the output unit 1111 displays images or outputs audio.

The receiving system illustrated in FIG. 128 as described above may be applied to, for example, a TV set (television receiver) that receives television broadcasting as digital broadcasting or a radio receiver that receives radio broadcasting.

Note that, if the signal acquired by the acquisition unit 1101 has not been subjected to compression encoding, a signal output from the transmission path decoding processing unit 1102 is supplied to the output unit 1111.

FIG. 129 is a block diagram illustrating a third example configuration of the receiving system to which the receiving device 12 is applicable.

Note that, in FIG. 129, portions corresponding to those illustrated in FIG. 127 are assigned the same reference numerals, and a description thereof will be omitted hereinafter, as appropriate.

The receiving system illustrated in FIG. 129 is common to that illustrated in FIG. 127 in that the acquisition unit 1101 and the transmission path decoding processing unit 1102 are included.

However, the receiving system illustrated in FIG. 129 is different from that illustrated in FIG. 127 in that the information source decoding processing unit 1103 is not included and a recording unit 1121 is further included.

The recording unit 1121 records (or stores) the signal (e.g., TS packets of an MPEG TS stream) output from the transmission path decoding processing unit 1102 on (or in) a recording (or storage) medium such as an optical disk, a hard disk (magnetic disk), or a flash memory.

The receiving system illustrated in FIG. 129 as described above may be applied to, for example, a recorder that records television broadcasting.

Note that, in FIG. 129, the receiving system may include the information source decoding processing unit 1103, and the recording unit 1121 is capable of recording a signal that has been subjected to an information source decoding process by the information source decoding processing unit 1103, that is, an image or audio obtained by decoding.

[Embodiment of Computer]

Next, the series of processes described above may be performed by hardware or software. If the series of processes is performed by software, a program constituting the software is installed into a general-purpose computer or the like.

Thus, FIG. 130 illustrates an example configuration of an embodiment of a computer into which a program for executing the series of processes described above is installed.

The program may be recorded in advance on a hard disk 705 or a ROM 703 serving as a recording medium incorporated in the computer.

Alternatively, the program may be temporarily or persistently stored in (or recorded on) a removable recording medium 711 such as a flexible disc, a CD-ROM (Compact Disc Read Only Memory), an MO (Magneto Optical) disc, a DVD (Digital Versatile Disc), a magnetic disk, or a semiconductor memory. The removable recording medium 711 may be provided as packaged software.

The program may be installed into the computer from the removable recording medium 711 described above, or may be wirelessly transferred to the computer from a download site via an artificial satellite for digital satellite broadcasting or transferred to the computer via a network such as a LAN (Local Area Network) or the Internet by wired connection. In the computer, the program transferred in the way described above may be received by a communication unit 708, and installed into the hard disk 705 incorporated in the computer.

The computer has a CPU (Central Processing Unit) 702 incorporated therein. An input/output interface 710 is connected to the CPU 702 via a bus 701. When an instruction is input by a user by, for example, operating an input unit 707 including a keyboard, a mouse, a microphone, and so forth via the input/output interface 710, the CPU 702 executes a program stored in the ROM (Read Only Memory) 703 in accordance with the instruction. Alternatively, the CPU 702 loads a program stored in the hard disk 705, a program transferred from a satellite or a network, received by the communication unit 708, and installed into the hard disk 705, or a program read from the removable recording medium 711 set in a drive 709 and installed into the hard disk 705 into a RAM (Random Access Memory) 704, and executes the loaded program. Accordingly, the CPU 702 performs processing according to the flowcharts described above or processing performed with the configurations in the block diagrams described above. Then, the CPU 702 outputs a result of the processing, if necessary, for example, from an output unit 706 including an LCD (Liquid Crystal Display), a speaker, and so forth via the input/output interface 710, transmits the result from the communication unit 708, or records the result on the hard disk 705.

It should be noted herein that processing steps describing a program for causing a computer to perform various kinds of processing may not necessarily be processed in a time-series manner in accordance with the order described herein in the flowcharts, and may also include processes executed in parallel or individually (for example, parallel processing or object-based processing).

In addition, a program may be processed by a single computer, or may be processed by a plurality of computers in a distributed manner. Furthermore, a program may also be transferred to and executed by a remote computer.

Note that embodiments of the present technology are not limited to the embodiments described above, and a variety of changes can be made without departing from the scope of the present technology.

More specifically, for example, the (parity check matrix initial value tables of) new LDPC codes described above may be used regardless of whether the communication path 13 (FIG. 7) is a satellite link, a terrestrial link, a cable (wired line), or any other unit. In addition, the new LDPC codes may also be used for data transmission other than digital broadcasting.

REFERENCE SIGNS LIST

11 transmitting device, 12 receiving device, 23 parity interleaver, 24 column twist interleaver, 25 demultiplexer, 31 memory, 32 permutation unit, 54 multiplexer, 55 column twist interleaver, 111 mode adaptation/multiplexer, 112 padder, 113 BB scrambler, 114 BCH encoder, 115 LDPC encoder, 116 bit interleaver, 117 QAM encoder, 118 time interleaver, 119 MISO/MIMO encoder, 120 frequency interleaver, 121 BCH encoder, 122 LDPC encoder, 123 QAM encoder, 124 frequency interleaver, 131 frame builder & resource allocation unit, 132 OFDM generation unit, 151 OFDM processing unit, 152 frame management unit, 153 frequency deinterleaver, 154 QAM decoder, 155 LDPC decoder, 156 BCH decoder, 161 frequency deinterleaver, 162 MISO/MIMO decoder, 163 time deinterleaver, 164 QAM decoder, 165 bit deinterleaver, 166 LDPC decoder, 167 BCH decoder, 168 BB descrambler, 169 null deletion unit, 170 demultiplexer, 300 edge data storage memory, 301 selector, 302 check node calculation unit, 303 cyclic shift circuit, 304 edge data storage memory, 305 selector, 306 received data memory, 307 variable node calculation unit, 308 cyclic shift circuit, 309 decoded word calculation unit, 310 received data reordering unit, 311 decoded data reordering unit, 601 encoding processing unit, 602 storage unit, 611 code rate setting unit, 612 initial value table read unit, 613 parity check matrix generation unit, 614 information bit read unit, 615 encoding parity computation unit, 616 control unit, 701 bus, 702 CPU, 703 ROM, 704 RAM, 705 hard disk, 706 output unit, 707 input unit, 708 communication unit, 709 drive, 710 input/output interface, 711 removable recording medium, 1001 inverse permutation unit, 1002 memory, 1011 parity deinterleaver, 1101 acquisition unit, 1101 transmission path decoding processing unit, 1103 information source decoding processing unit, 1111 output unit, 1121 recording unit 

1. A data processing apparatus comprising: an encoding unit configured to encode information bits into an LDPC (Low Density Parity Check) code having a code length of 64800 bits and a code rate of 18/30 on the basis of a parity check matrix of the LDPC code, wherein the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table showing positions of elements of 1 in the information matrix portion in units of 360 columns, including 113 1557 3316 5680 6241 10407 13404 13947 14040 14353 15522 15698 16079 17363 19374 19543 20530 22833 24339 271 1361 6236 7006 7307 7333 12768 15441 15568 17923 18341 20321 21502 22023 23938 25351 25590 25876 25910 73 605 872 4008 6279 7653 10346 10799 12482 12935 13604 15909 16526 19782 20506 22804 23629 24859 25600 1445 1690 4304 4851 8919 9176 9252 13783 16076 16675 17274 18806 18882 20819 21958 22451 23869 23999 24177 1290 2337 5661 6371 8996 10102 10941 11360 12242 14918 16808 20571 23374 24046 25045 25060 25662 25783 25913 28 42 1926 3421 3503 8558 9453 10168 15820 17473 19571 19685 22790 23336 23367 23890 24061 25657 25680 0 1709 4041 4932 5968 7123 8430 9564 10596 11026 14761 19484 20762 20858 23803 24016 24795 25853 25863 29 1625 6500 6609 16831 18517 18568 18738 19387 20159 20544 21603 21941 24137 24269 24416 24803 25154 25395 55 66 871 3700 11426 13221 15001 16367 17601 18380 22796 23488 23938 25476 25635 25678 25807 25857 25872 1 19 5958 8548 8860 11489 16845 18450 18469 19496 20190 23173 25262 25566 25668 25679 25858 25888 25915 7520 7690 8855 9183 14654 16695 17121 17854 18083 18428 19633 20470 20736 21720 22335 23273 25083 25293 25403 48 58 410 1299 3786 10668 18523 18963 20864 22106 22308 23033 23107 23128 23990 24286 24409 24595 25802 12 51 3894 6539 8276 10885 11644 12777 13427 14039 15954 17078 19053 20537 22863 24521 25087 25463 25838 3509 8748 9581 11509 15884 16230 17583 19264 20900 21001 21310 22547 22756 22959 24768 24814 25594 25626 25880 21 29 69 1448 2386 4601 6626 6667 10242 13141 13852 14137 18640 19951 22449 23454 24431 25512 25814 18 53 7890 9934 10063 16728 19040 19809 20825 21522 21800 23582 24556 25031 25547 25562 25733 25789 25906 4096 4582 5766 5894 6517 10027 12182 13247 15207 17041 18958 20133 20503 22228 24332 24613 25689 25855 25883 0 25 819 5539 7076 7536 7695 9532 13668 15051 17683 19665 20253 21996 24136 24890 25758 25784 25807 34 40 44 4215 6076 7427 7965 8777 11017 15593 19542 22202 22973 23397 23423 24418 24873 25107 25644 1595 6216 22850 25439 1562 15172 19517 22362 7508 12879 24324 24496 6298 15819 16757 18721 11173 15175 19966 21195 59 13505 16941 23793 2267 4830 12023 20587 8827 9278 13072 16664 14419 17463 23398 25348 6112 16534 20423 22698 493 8914 21103 24799 6896 12761 13206 25873 2 1380 12322 21701 11600 21306 25753 25790 8421 13076 14271 15401 9630 14112 19017 20955 212 13932 21781 25824 5961 9110 16654 19636 58 5434 9936 12770 6575 11433 19798 2731 7338 20926 14253 18463 25404 21791 24805 25869 2 11646 15850 6075 8586 23819 18435 22093 24852 2103 2368 11704 10925 17402 18232 9062 25061 25674 18497 20853 23404 18606 19364 19551 7 1022 25543 6744 15481 25868 9081 17305 25164 8 23701 25883 9680 19955 22848 56 4564 19121 5595 15086 25892 3174 17127 23183 19397 19817 20275 12561 24571 25825 7111 9889 25865 19104 20189 21851 549 9686 25548 6586 20325 25906 3224 20710 21637 641 15215 25754 13484 23729 25818 2043 7493 24246 16860 25230 25768 22047 24200 24902 9391 18040 19499 7855 24336 25069 23834 25570 25852 1977 8800 25756 6671 21772 25859 3279 6710 24444 24099 25117 25820 5553 12306 25915 48 11107 23907 10832 11974 25773 2223 17905 25484 16782 17135 20446 475 2861 3457 16218 22449 24362 11716 22200 25897 8315 15009 22633 13 20480 25852 12352 18658 25687 3681 14794 23703 30 24531 25846 4103 22077 24107 23837 25622 25812 3627 13387 25839 908 5367 19388 0 6894 25795 20322 23546 25181 8178 25260 25437 2449 13244 22565 31 18928 22741 1312 5134 14838 6085 13937 24220 66 14633 25670 47 22512 25472 8867 24704 25279 6742 21623 22745 147 9948 24178 8522 24261 24307 19202 22406
 24609. 